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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 2701. |
If G and G' be the centroids of the triangles ABC and \[A'B'C'\] respectively, then \[\overrightarrow{AA}'+\overrightarrow{BB'}+\overrightarrow{CC}'=\] |
| A. | \[\frac{2}{3}\overrightarrow{GG}'\] |
| B. | \[\overrightarrow{GG}'\] |
| C. | \[2\,\overrightarrow{GG}'\] |
| D. | \[3\,\overrightarrow{GG}'\] |
| Answer» E. | |
| 2702. |
If \[\mathbf{a}=\mathbf{i}+2\mathbf{j}+2\mathbf{k}\] and \[\mathbf{b}=3\mathbf{i}+6\mathbf{j}+2\mathbf{k},\] then a vector in the direction of a and having magnitude as |b| is [IIT 1983] |
| A. | \[7\,(\mathbf{i}+\mathbf{j}+\mathbf{k})\] |
| B. | \[\frac{7}{3}\,(\mathbf{i}+2\mathbf{j}+2\mathbf{k})\] |
| C. | \[\frac{7}{9}\,(\mathbf{i}+2\mathbf{j}+2\,\mathbf{k})\] |
| D. | None of these |
| Answer» C. \[\frac{7}{9}\,(\mathbf{i}+2\mathbf{j}+2\,\mathbf{k})\] | |
| 2703. |
If the position vector of one end of the line segment AB be \[2\mathbf{i}+3\mathbf{j}-\mathbf{k}\] and the position vector of its middle point be \[3\,(\mathbf{i}+\mathbf{j}+\mathbf{k}),\] then the position vector of the other end is |
| A. | \[4\mathbf{i}+3\mathbf{j}+5\mathbf{k}\] |
| B. | \[4\mathbf{i}-3\mathbf{j}+7\mathbf{k}\] |
| C. | \[4\mathbf{i}+3\mathbf{j}+7\mathbf{k}\] |
| D. | \[4\mathbf{i}+3\mathbf{j}-7\mathbf{k}\] |
| Answer» D. \[4\mathbf{i}+3\mathbf{j}-7\mathbf{k}\] | |
| 2704. |
If the position vectors of the points A, B, C, D be \[2\mathbf{i}+3\mathbf{j}+5\mathbf{k},\] \[\mathbf{i}+2\mathbf{j}+3\mathbf{k},\,\,-5\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] and \[\mathbf{i}+10\mathbf{j}+10\mathbf{k}\] respectively, then [MNR 1982] |
| A. | \[\overrightarrow{AB}=\overrightarrow{CD}\] |
| B. | \[\overrightarrow{AB}\,\,\,|\,\,|\,\,\,\overrightarrow{\,CD}\] |
| C. | \[\overrightarrow{AB}\,\,\bot \,\,\overrightarrow{CD}\] |
| D. | None of these |
| Answer» C. \[\overrightarrow{AB}\,\,\bot \,\,\overrightarrow{CD}\] | |
| 2705. |
P is the point of intersection of the diagonals of the parallelogram ABCD. If O is any point, then \[\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}=\] [RPET 1989; J & K 2005] |
| A. | \[\overrightarrow{OP}\] |
| B. | \[2\,\,\overrightarrow{OP}\] |
| C. | \[3\,\,\overrightarrow{OP}\] |
| D. | \[4\,\,\overrightarrow{OP}\] |
| Answer» E. | |
| 2706. |
If the position vectors of the point A, B, C be i, j, k respectively and P be a point such that \[\overrightarrow{AB}=\overrightarrow{CP},\] then the position vector of P is |
| A. | \[-\mathbf{i}+\mathbf{j}+\mathbf{k}\] |
| B. | \[-\mathbf{i}-\mathbf{j}+\mathbf{k}\] |
| C. | \[\mathbf{i}+\mathbf{j}-\mathbf{k}\] |
| D. | None of these |
| Answer» B. \[-\mathbf{i}-\mathbf{j}+\mathbf{k}\] | |
| 2707. |
If ABCD is a parallelogram and the position vectors of A, B, C are \[\mathbf{i}+3\mathbf{j}+5\mathbf{k},\,\,\mathbf{i}+\mathbf{j}+\mathbf{k}\] and \[7\mathbf{i}+7\mathbf{j}+7\mathbf{k},\] then the position vector of D will be |
| A. | \[7\mathbf{i}+5\mathbf{j}+3\mathbf{k}\] |
| B. | \[7\mathbf{i}+9\mathbf{j}+11\mathbf{k}\] |
| C. | \[9\mathbf{i}+11\mathbf{j}+13\mathbf{k}\] |
| D. | \[8\mathbf{i}+8\mathbf{j}+8\mathbf{k}\] |
| Answer» C. \[9\mathbf{i}+11\mathbf{j}+13\mathbf{k}\] | |
| 2708. |
If in the given figure \[\overrightarrow{OA}=\mathbf{a},\,\,\,\overrightarrow{OB}=\mathbf{b}\] and \[AP\,\,:\,\,PB=m\,\,:\,\,n,\] then \[\overrightarrow{OP}=\] [RPET 1981; MP PET 1988] |
| A. | \[\frac{m\,\mathbf{a}+n\,\mathbf{b}}{m+n}\] |
| B. | \[\frac{n\,\mathbf{a}+m\,\mathbf{b}}{m+n}\] |
| C. | \[m\,\mathbf{a}-n\,\mathbf{b}\] |
| D. | \[\frac{m\,\mathbf{a}-n\,\mathbf{b}}{m-n}\] |
| Answer» C. \[m\,\mathbf{a}-n\,\mathbf{b}\] | |
| 2709. |
The position vectors of A and B are \[\mathbf{i}-\mathbf{j}+2\mathbf{k}\] and \[3\mathbf{i}-\mathbf{j}+3\mathbf{k}.\] The position vector of the middle point of the line AB is [MP PET 1988] |
| A. | \[\frac{1}{2}\mathbf{i}-\frac{1}{2}\mathbf{j}+\mathbf{k}\] |
| B. | \[2\mathbf{i}-\mathbf{j}+\frac{5}{2}\mathbf{k}\] |
| C. | \[\frac{3}{2}\mathbf{i}-\frac{1}{2}\mathbf{j}+\frac{3}{2}\mathbf{k}\] |
| D. | None of these |
| Answer» C. \[\frac{3}{2}\mathbf{i}-\frac{1}{2}\mathbf{j}+\frac{3}{2}\mathbf{k}\] | |
| 2710. |
If a and b are the position vectors of A and B respectively, then the position vector of a point C on AB produced such that \[\overrightarrow{AC}=3\overrightarrow{AB}\] is [MNR 1980; MP PET 1995, 99] |
| A. | \[3\mathbf{a}-\mathbf{b}\] |
| B. | \[3\mathbf{b}-\mathbf{a}\] |
| C. | \[3\mathbf{a}-2\mathbf{b}\] |
| D. | \[3\mathbf{b}-2\mathbf{a}\] |
| Answer» E. | |
| 2711. |
If D, E, F be the middle points of the sides BC, CA and AB of the triangle ABC, then \[\overrightarrow{AD}+\overrightarrow{BE}+\overrightarrow{CF}\] is |
| A. | A zero vector |
| B. | A unit vector |
| C. | 0 |
| D. | None of these |
| Answer» B. A unit vector | |
| 2712. |
If a, b, c are the position vectors of the vertices A, B, C of the triangle ABC, then the centroid of \[\Delta \,ABC\] is [MP PET 1987] |
| A. | \[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3}\] |
| B. | \[\frac{1}{2}\,\left( \mathbf{a}+\frac{\mathbf{b}+\mathbf{c}}{2} \right)\] |
| C. | \[\mathbf{a}+\frac{\mathbf{b}+\mathbf{c}}{2}\] |
| D. | \[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{2}\] |
| Answer» B. \[\frac{1}{2}\,\left( \mathbf{a}+\frac{\mathbf{b}+\mathbf{c}}{2} \right)\] | |
| 2713. |
The unit vector parallel to the resultant vector of \[2\mathbf{i}+4\mathbf{j}-5\mathbf{k}\] and \[\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] is [MP PET 2003] |
| A. | \[\frac{1}{7}\,(3\mathbf{i}+6\mathbf{j}-2\mathbf{k})\] |
| B. | \[\frac{\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{3}}\] |
| C. | \[\frac{\mathbf{i}+\mathbf{j}+2\mathbf{k}}{\sqrt{6}}\] |
| D. | \[\frac{1}{\sqrt{69}}\,(-\mathbf{i}-\mathbf{j}+8\mathbf{k})\] |
| Answer» B. \[\frac{\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{3}}\] | |
| 2714. |
If \[\mathbf{a}+\mathbf{b}\] bisects the angle between a and b, then a and b are |
| A. | Mutually perpendicular |
| B. | Unlike vectors |
| C. | Equal in magnitude |
| D. | None of these |
| Answer» D. None of these | |
| 2715. |
Five points given by A, B, C, D, E are in a plane. Three forces \[\overrightarrow{AC},\,\,\overrightarrow{AD}\] and \[\overrightarrow{AE}\] act at A and three forces \[\overrightarrow{CB},\,\,\overrightarrow{DB},\,\,\overrightarrow{EB}\] act at B. Then their resultant is [AMU 2001] |
| A. | \[2\overrightarrow{AC}\] |
| B. | \[3\overrightarrow{AB}\] |
| C. | \[3\overrightarrow{DB}\] |
| D. | \[2\overrightarrow{BC}\] |
| Answer» C. \[3\overrightarrow{DB}\] | |
| 2716. |
The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12N. The magnitude of the two forces are [AIEEE 2002] |
| A. | 13, 5 |
| B. | 12, 6 |
| C. | 14, 4 |
| D. | 11, 7 |
| Answer» B. 12, 6 | |
| 2717. |
If \[\mathbf{a}=3\mathbf{i}-2\mathbf{j}+\mathbf{k},\,\,\mathbf{b}=2\mathbf{i}-4\mathbf{j}-3\mathbf{k}\] and \[\mathbf{c}=-\mathbf{i}+2\mathbf{j}+2\mathbf{k},\] then \[\mathbf{a}+\mathbf{b}+\mathbf{c}\] is [MP PET 2001] |
| A. | \[3\mathbf{i}-4\mathbf{j}\] |
| B. | \[3\mathbf{i}+4\mathbf{j}\] |
| C. | \[4\mathbf{i}-4\mathbf{j}\] |
| D. | \[4\mathbf{i}+4\mathbf{j}\] |
| Answer» D. \[4\mathbf{i}+4\mathbf{j}\] | |
| 2718. |
A, B, C, D, E are five coplanar points, then \[\overrightarrow{DA}+\overrightarrow{DB}+\overrightarrow{DC}+\overrightarrow{AE}+\overrightarrow{BE}+\overrightarrow{CE}\] is equal to [RPET 1999] |
| A. | \[\overrightarrow{DE}\] |
| B. | \[3\,\overrightarrow{DE}\] |
| C. | \[2\,\overrightarrow{DE}\] |
| D. | \[4\,\overrightarrow{ED}\] |
| Answer» C. \[2\,\overrightarrow{DE}\] | |
| 2719. |
If \[\mathbf{a}=2\mathbf{i}+\mathbf{j}-8\mathbf{k}\] and \[\mathbf{b}=\mathbf{i}+3\mathbf{j}-4\mathbf{k},\] then the magnitude of \[\mathbf{a}+\mathbf{b}=\] [MP PET 1996] |
| A. | 13 |
| B. | \[\frac{13}{3}\] |
| C. | \[\frac{3}{13}\] |
| D. | \[\frac{4}{13}\] |
| Answer» B. \[\frac{13}{3}\] | |
| 2720. |
In a trapezium, the vector \[\overrightarrow{BC}=\lambda \overrightarrow{AD}.\] We will then find that \[\mathbf{p}=\overrightarrow{AC}+\overrightarrow{BD}\] is collinear with \[\overrightarrow{AD},\] If \[\mathbf{p}=\mu \overrightarrow{AD},\] then |
| A. | \[\mu =\lambda +1\] |
| B. | \[\lambda =\mu +1\] |
| C. | \[\lambda +\mu =1\] |
| D. | \[\mu =2+\lambda \] |
| Answer» B. \[\lambda =\mu +1\] | |
| 2721. |
\[\mathbf{p}=2\mathbf{a}-3\mathbf{b},\,\,\,\mathbf{q}=\mathbf{a}-2\mathbf{b}+\mathbf{c},\,\,\mathbf{r}=-3\mathbf{a}+\mathbf{b}+2\mathbf{c};\] where a, b and c being non-zero, non-coplanar vectors, then the vector \[-2\mathbf{a}+3\mathbf{b}-\mathbf{c}\] is equal to |
| A. | \[\mathbf{p}-4\mathbf{q}\] |
| B. | \[\frac{-7\mathbf{q}+\mathbf{r}}{5}\] |
| C. | \[2\mathbf{p}-3\mathbf{q}+\mathbf{r}\] |
| D. | \[4\mathbf{p}-2\mathbf{r}\] |
| Answer» C. \[2\mathbf{p}-3\mathbf{q}+\mathbf{r}\] | |
| 2722. |
\[3\,\,\overrightarrow{OD}+\overrightarrow{DA}+\overrightarrow{DB}+\overrightarrow{DC}=\] [IIT 1988] |
| A. | \[\overrightarrow{OA}+\overrightarrow{OB}-\overrightarrow{OC}\] |
| B. | \[\overrightarrow{OA}+\overrightarrow{OB}-\overrightarrow{BD}\] |
| C. | \[\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}\] |
| D. | None of these |
| Answer» D. None of these | |
| 2723. |
In a regular hexagon ABCDEF, \[\overrightarrow{AE}=\] [MNR 1984] |
| A. | \[2\mathbf{a}-3\mathbf{b}\] |
| B. | \[\overrightarrow{AC}\,\,+\,\,\overrightarrow{AF}\,\,-\,\overrightarrow{AB}\] |
| C. | \[\overrightarrow{AC}\,\,+\,\,\overrightarrow{AB}\,\,-\,\,\overrightarrow{AF}\] |
| D. | None of these |
| Answer» C. \[\overrightarrow{AC}\,\,+\,\,\overrightarrow{AB}\,\,-\,\,\overrightarrow{AF}\] | |
| 2724. |
Which of the following is not a unit vector for all values of q |
| A. | \[(\cos \theta )\mathbf{i}-(\sin \theta )\,\mathbf{j}\] |
| B. | \[(\sin \theta )\,\mathbf{i}+(\cos \theta )\,\mathbf{j}\] |
| C. | \[(\sin \,\,2\theta )\,\mathbf{i}-(\cos \theta )\,\mathbf{j}\] |
| D. | \[(\cos \,\,2\theta )\,\mathbf{i}-(\sin \,\,2\theta )\,\mathbf{j}\] |
| Answer» D. \[(\cos \,\,2\theta )\,\mathbf{i}-(\sin \,\,2\theta )\,\mathbf{j}\] | |
| 2725. |
What should be added in vector \[\mathbf{a}=3\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] to get its resultant a unit vector i [Roorkee 1977] |
| A. | \[-\,2\mathbf{i}-4\mathbf{j}+2\mathbf{k}\] |
| B. | \[-2\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] |
| C. | \[2\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] |
| D. | None of these |
| Answer» B. \[-2\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] | |
| 2726. |
If \[\mathbf{a}=\mathbf{i}+2\mathbf{j}+3\mathbf{k},\,\,\,\mathbf{b}=-\mathbf{i}+2\mathbf{j}+\mathbf{k}\] and \[\mathbf{c}=3\mathbf{i}+\mathbf{j},\] then the unit vector along its resultant is [Roorkee 1980] |
| A. | \[3\mathbf{i}+5\mathbf{j}+4\mathbf{k}\] |
| B. | \[\frac{3\mathbf{i}+5\mathbf{j}+4\mathbf{k}}{50}\] |
| C. | \[\frac{3\mathbf{i}+5\mathbf{j}+4\mathbf{k}}{5\sqrt{2}}\] |
| D. | None of these |
| Answer» D. None of these | |
| 2727. |
If \[\mathbf{a}=2\mathbf{i}+5\mathbf{j}\] and \[\mathbf{b}=2\mathbf{i}-\mathbf{j},\] then the unit vector along \[y=0\] will be [RPET 1985, 95] |
| A. | \[\frac{\mathbf{i}-\mathbf{j}}{\sqrt{2}}\] |
| B. | \[ap+bq+cr=0\] |
| C. | \[{{90}^{o}}\] |
| D. | \[\frac{\mathbf{i}+\mathbf{j}}{\sqrt{2}}\] |
| Answer» E. | |
| 2728. |
If a, b and c be three non-zero vectors, no two of which are collinear. If the vector \[\mathbf{a}+2\mathbf{b}\] is collinear with c and \[\mathbf{b}+3\mathbf{c}\] is collinear with a, then (\[\lambda \] being some non-zero scalar) \[\mathbf{a}+2\mathbf{b}+6\mathbf{c}\] is equal to [AIEEE 2004] |
| A. | \[\lambda \mathbf{a}\] |
| B. | \[\lambda \mathbf{b}\] |
| C. | \[\lambda \mathbf{c}\] |
| D. | 0 |
| Answer» E. | |
| 2729. |
A vector coplanar with the non-collinear vectors a and b is |
| A. | \[\mathbf{a}\times \mathbf{b}\] |
| B. | \[l\ne 0,\,\,m\ne 0,\,\,n\ne 0\] |
| C. | \[\mathbf{a}\,.\,\mathbf{b}\] |
| D. | None of these |
| Answer» C. \[\mathbf{a}\,.\,\mathbf{b}\] | |
| 2730. |
If ABCD is a parallelogram, \[\overrightarrow{AB}=2\,\mathbf{i}+4\,\mathbf{j}-5\,\mathbf{k}\] and \[\overrightarrow{AD}=\,\mathbf{i}+2\,\mathbf{j}+3\,\mathbf{k},\] then the unit vector in the direction of BD is [Roorkee 1976] |
| A. | \[\frac{1}{\sqrt{69}}\,(\mathbf{i}+2\mathbf{j}-8\mathbf{k})\] |
| B. | \[\frac{1}{69}\,(\mathbf{i}+2\mathbf{j}-8\,\mathbf{k})\] |
| C. | \[\frac{1}{\sqrt{69}}\,(-\mathbf{i}-2\mathbf{j}+8\mathbf{k})\] |
| D. | \[\frac{1}{69}\,(-\mathbf{i}-2\mathbf{j}+8\,\mathbf{k})\] |
| Answer» D. \[\frac{1}{69}\,(-\mathbf{i}-2\mathbf{j}+8\,\mathbf{k})\] | |
| 2731. |
In the figure, a vector x satisfies the equation \[\mathbf{x}-\mathbf{w}=\mathbf{v}\]. Then x = |
| A. | \[2\mathbf{a}+\mathbf{b}+\mathbf{c}\] |
| B. | \[\mathbf{a}+2\mathbf{b}+\mathbf{c}\] |
| C. | \[\mathbf{a}+\mathbf{b}+2\mathbf{c}\] |
| D. | \[\mathbf{a}+\mathbf{b}+\mathbf{c}\] |
| Answer» C. \[\mathbf{a}+\mathbf{b}+2\mathbf{c}\] | |
| 2732. |
If P and Q be the middle points of the sides BC and CD of the parallelogram ABCD, then \[\overrightarrow{AP}+\overrightarrow{AQ}=\] |
| A. | \[\overrightarrow{AC}\] |
| B. | \[\frac{1}{2}\overrightarrow{AC}\] |
| C. | \[\frac{2}{3}\overrightarrow{AC}\] |
| D. | \[\frac{3}{2}\overrightarrow{AC}\] |
| Answer» E. | |
| 2733. |
ABC is an isosceles triangle right angled at A. Forces of magnitude \[2\sqrt{2,}\,5\] and 6 act along \[\overrightarrow{BC},\,\,\overrightarrow{CA}\] and \[\overrightarrow{AB}\] respectively. The magnitude of their resultant force is [Roorkee 1999] |
| A. | 4 |
| B. | 5 |
| C. | \[11+2\sqrt{2}\] |
| D. | 30 |
| Answer» C. \[11+2\sqrt{2}\] | |
| 2734. |
If \[\mathbf{a}=2\mathbf{i}+2\mathbf{j}-\mathbf{k}\] and \[|x\,\mathbf{a}|\,\,=1,\] then x = |
| A. | \[\pm \frac{1}{3}\] |
| B. | \[\pm \frac{1}{4}\] |
| C. | \[\pm \frac{1}{5}\] |
| D. | \[\pm \frac{1}{6}\] |
| Answer» B. \[\pm \frac{1}{4}\] | |
| 2735. |
If ABCDEF is a regular hexagon and \[\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}=\lambda \,\overrightarrow{AD},\] then \[\lambda =\] [RPET 1985] |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 6 |
| Answer» C. 4 | |
| 2736. |
If the position vectors of the vertices A, B, C of a triangle ABC are \[7\mathbf{j}+10\mathbf{k},\] \[-\mathbf{i}+6\mathbf{j}+6\mathbf{k}\] and \[-4\mathbf{i}+9\mathbf{j}+6\mathbf{k}\] respectively, the triangle is [UPSEAT 2004] |
| A. | Equilateral |
| B. | Isosceles |
| C. | Scalene |
| D. | Right angled and isosceles also |
| Answer» E. | |
| 2737. |
The vectors \[\overrightarrow{AB}=3\mathbf{i}+4\mathbf{k},\] and \[\overrightarrow{AC}=5\mathbf{i}-2\mathbf{j}+4\mathbf{k}\] are the sides of a triangle ABC. The length of the median through A is [AIEEE 2003] |
| A. | \[\sqrt{18}\] |
| B. | \[\sqrt{72}\] |
| C. | \[\sqrt{33}\] |
| D. | \[\sqrt{288}\] |
| Answer» D. \[\sqrt{288}\] | |
| 2738. |
The position vectors of the points A, B, C are \[(2\mathbf{i}+\mathbf{j}-\mathbf{k}),\] \[(3\mathbf{i}-2\mathbf{j}+\mathbf{k})\] and \[(\mathbf{i}+4\mathbf{j}-3\mathbf{k})\] respectively. These points [Kurukshetra CEE 2002] |
| A. | Form an isosceles triangle |
| B. | Form a right-angled triangle |
| C. | Are collinear |
| D. | Form a scalene triangle |
| Answer» D. Form a scalene triangle | |
| 2739. |
The position vectors of A and B are \[2\mathbf{i}-9\mathbf{j}-4\mathbf{k}\] and \[6\mathbf{i}-3\mathbf{j}+8\mathbf{k}\] respectively, then the magnitude of \[\overrightarrow{AB}\] is [MP PET 2000] |
| A. | 11 |
| B. | 12 |
| C. | 13 |
| D. | 14 |
| Answer» E. | |
| 2740. |
If a is non zero vector of modulus a and m is a non-zero scalar, then ma is a unit vector if [MP PET 2002] |
| A. | \[m=\pm 1\] |
| B. | \[m=\,\,|\mathbf{a}|\] |
| C. | \[m=\frac{1}{|\mathbf{a}|}\] |
| D. | \[m=\pm \,2\] |
| Answer» D. \[m=\pm \,2\] | |
| 2741. |
The direction cosines of the vector \[3\mathbf{i}-4\mathbf{j}+5\mathbf{k}\] are [Karnataka CET 2000] |
| A. | \[\frac{3}{5},\,\frac{-4}{5},\frac{1}{5}\] |
| B. | \[\frac{3}{5\sqrt{2}},\,\frac{-4}{5\sqrt{2}},\frac{1}{\sqrt{2}}\] |
| C. | \[\frac{3}{\sqrt{2}},\,\frac{-4}{\sqrt{2}},\,\frac{1}{\sqrt{2}}\] |
| D. | \[\frac{3}{5\sqrt{2}},\,\,\frac{4}{5\sqrt{2}},\,\frac{1}{\sqrt{2}}\] |
| Answer» C. \[\frac{3}{\sqrt{2}},\,\frac{-4}{\sqrt{2}},\,\frac{1}{\sqrt{2}}\] | |
| 2742. |
If the resultant of two forces of magnitudes P and Q acting at a point at an angle of \[{{60}^{o}}\] is \[\sqrt{7}Q,\] then P/Q is [Roorkee 1999] |
| A. | 1 |
| B. | \[\frac{3}{2}\] |
| C. | 2 |
| D. | 4 |
| Answer» D. 4 | |
| 2743. |
If the vectors \[6\mathbf{i}-2\mathbf{j}+3\mathbf{k},\,\,2\mathbf{i}+3\mathbf{j}-6\mathbf{k}\] and \[3\mathbf{i}+6\mathbf{j}-2\mathbf{k}\] form a triangle, then it is [Karnataka CET 1999] |
| A. | Right angled |
| B. | Obtuse angled |
| C. | Equilteral |
| D. | Isosceles |
| Answer» C. Equilteral | |
| 2744. |
If one side of a square be represented by the vector \[3\mathbf{i}+4\mathbf{j}+5\mathbf{k},\] then the area of the square is |
| A. | 12 |
| B. | 13 |
| C. | 25 |
| D. | 50 |
| Answer» E. | |
| 2745. |
If a and b are two non-zero and non-collinear vectors, then a + b and a ? b are [MP PET 1997] |
| A. | Linearly dependent vectors |
| B. | Linearly independent vectors |
| C. | Linearly dependent and independent vectors |
| D. | None of these |
| Answer» C. Linearly dependent and independent vectors | |
| 2746. |
If OP = 8 and \[\overrightarrow{OP}\] makes angles \[{{45}^{o}}\] and \[{{60}^{o}}\] with OX-axis and OY-axis respectively, then \[\overrightarrow{OP}=\] |
| A. | \[8\,(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] |
| B. | \[4\,(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] |
| C. | \[\frac{1}{4}(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] |
| D. | \[\frac{1}{8}(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] |
| Answer» C. \[\frac{1}{4}(\sqrt{2}\mathbf{i}+\mathbf{j}\pm \mathbf{k})\] | |
| 2747. |
If \[|\mathbf{a}|\,\,=3,\,\,\,|\mathbf{b}|\,\,=4\] and \[|\mathbf{a}+\mathbf{b}|\,\,=5,\] then \[|\mathbf{a}-\mathbf{b}|\,\,=\] [EAMCET 1994] |
| A. | 6 |
| B. | 5 |
| C. | 4 |
| D. | 3 |
| Answer» C. 4 | |
| 2748. |
The point having position vectors \[2\mathbf{i}+3\mathbf{j}+4\mathbf{k},\,\,\]\[3\mathbf{i}+4\mathbf{j}+2\mathbf{k},\] \[4\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] are the vertices of [EAMCET 1988] |
| A. | Right angled triangle |
| B. | Isosceles triangle |
| C. | Equilateral triangle |
| D. | Collinear |
| Answer» D. Collinear | |
| 2749. |
The direction cosines of vector \[\mathbf{a}=3\mathbf{i}+4\mathbf{j}+5\mathbf{k}\] in the direction of positive axis of x, is [MP PET 1991] |
| A. | \[\pm \frac{3}{\sqrt{50}}\] |
| B. | \[\frac{4}{\sqrt{50}}\] |
| C. | \[\frac{3}{\sqrt{50}}\] |
| D. | \[-\frac{4}{\sqrt{50}}\] |
| Answer» D. \[-\frac{4}{\sqrt{50}}\] | |
| 2750. |
If the resultant of two forces is of magnitude P and equal to one of them and perpendicular to it, then the other force is [MNR 1986] |
| A. | \[P\sqrt{2}\] |
| B. | P |
| C. | \[P\sqrt{3}\] |
| D. | None of these |
| Answer» B. P | |