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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.
| 7401. |
Let \[{{x}^{2}}+3{{y}^{2}}=3\] be the equation of an ellipse in the x-y plane. A and B are two points whose position vectors are \[-\sqrt{3}\hat{i}\] and\[-\sqrt{3}\hat{i}+2\hat{k}\]. Then the position vector of a point P on the ellipse such that \[\angle APB=\pi /4\] is |
| A. | \[\pm \hat{j}\] |
| B. | \[\pm (\hat{i}+\hat{j})\] |
| C. | \[\pm \,\hat{i}\] |
| D. | None of these |
| Answer» B. \[\pm (\hat{i}+\hat{j})\] | |
| 7402. |
Let \[\alpha ,\beta ,\gamma \] be distinct real numbers. The points with position vectors \[\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k},\beta \hat{i}+\gamma \hat{j}+\alpha \hat{k}\] and \[\gamma \hat{i}+\alpha \hat{j}+\beta \hat{k}\] |
| A. | Are collinear |
| B. | Form an equilateral triangle |
| C. | Form a scalene triangle |
| D. | Form a right-angled triangle |
| Answer» B. Form an equilateral triangle | |
| 7403. |
In a right angle \[\Delta ABC,\text{ }\angle A=90{}^\circ \] and sides a, b, c are respectively, 5 cm, 4 cm and 3 cm. If a force \[\vec{F}\] has moments 0, 9 and 16 in N cm. units respectively about vertices A, B and C, then magnitude of \[\vec{F}\] is |
| A. | 9 |
| B. | 4 |
| C. | 5 |
| D. | 3 |
| Answer» D. 3 | |
| 7404. |
If ABCDEF is a regular hexagon and\[\overrightarrow{AB}+\overrightarrow{AC}+\overrightarrow{AD}+\overrightarrow{AE}+\overrightarrow{AF}=k\overrightarrow{AD}\], then find the value of k. |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 5 |
| Answer» C. 4 | |
| 7405. |
The projection of a along b is [RPET 1995] |
| A. | \[\frac{\mathbf{a}\,.\,\mathbf{b}}{|\mathbf{a}|}\] |
| B. | \[\frac{\mathbf{a}\,\times \,\mathbf{b}}{|\mathbf{a}|}\] |
| C. | \[\frac{\mathbf{a}\,.\,\mathbf{b}}{|\mathbf{b}|}\] |
| D. | \[\frac{\mathbf{a}\,\times \,\mathbf{b}}{|\mathbf{b}|}\] |
| Answer» D. \[\frac{\mathbf{a}\,\times \,\mathbf{b}}{|\mathbf{b}|}\] | |
| 7406. |
If \[\mathbf{a}=4\mathbf{i}+6\mathbf{j}\] and \[\mathbf{b}=3\,\mathbf{j}+4\,\mathbf{k},\] then the component of a along b is [IIT Screening 1989; MNR 1983, 87; UPSEAT 2000] |
| A. | \[\frac{18}{10\sqrt{3}}(3\mathbf{j}+4\mathbf{k})\] |
| B. | \[\frac{18}{25}(3\mathbf{j}+4\mathbf{k})\] |
| C. | \[\frac{18}{\sqrt{3}}(3\mathbf{j}+4\mathbf{k})\] |
| D. | \[(3\mathbf{j}+4\mathbf{k})\] |
| Answer» C. \[\frac{18}{\sqrt{3}}(3\mathbf{j}+4\mathbf{k})\] | |
| 7407. |
A unit vector in the \[xy-\]plane which is perpendicular to \[4\mathbf{i}-3\mathbf{j}+\mathbf{k}\] is [RPET 1991] |
| A. | \[\frac{\mathbf{i}+\mathbf{j}}{\sqrt{2}}\] |
| B. | \[\frac{1}{5}(3\mathbf{i}+4\mathbf{j})\] |
| C. | \[\frac{1}{5}\,(3\mathbf{i}-4\mathbf{j})\] |
| D. | None of these |
| Answer» C. \[\frac{1}{5}\,(3\mathbf{i}-4\mathbf{j})\] | |
| 7408. |
If the vectors \[a\mathbf{i}+2\mathbf{j}+3\mathbf{k}\] and \[-\mathbf{i}+5\mathbf{j}+a\mathbf{k}\] are perpendicular to each other, then \[a=\] [MP PET 1996] |
| A. | 6 |
| B. | ? 6 |
| C. | 5 |
| D. | ? 5 |
| Answer» E. | |
| 7409. |
If \[\mathbf{a}\ne \mathbf{0},\,\,\mathbf{b}\ne \mathbf{0}\] and \[|\mathbf{a}+\mathbf{b}|\,=\,|\mathbf{a}-\mathbf{b}|,\] then the vectors a and b are [Roorkee 1986; MNR 1988; IIT Screening 1989; MP PET 1990, 97; RPET 1984, 90, 96, 99; KCET 1999] |
| A. | Parallel to each other |
| B. | Perpendicular to each other |
| C. | Inclined at an angle of \[{{60}^{o}}\] |
| D. | Neither perpendicular nor parallel |
| Answer» C. Inclined at an angle of \[{{60}^{o}}\] | |
| 7410. |
If the vectors \[a\,\mathbf{i}-2\mathbf{j}+3\mathbf{k}\] and \[3\mathbf{i}+6\mathbf{j}-5\mathbf{k}\] are perpendicular to each other, then a is given by [MP PET 1993] |
| A. | 9 |
| B. | 16 |
| C. | 25 |
| D. | 36 |
| Answer» B. 16 | |
| 7411. |
Let a and b be two unit vectors inclined at an angle \[\theta \], then \[\sin \,(\theta /2)\] is equal to [BIT Ranchi 1991; Karnataka CET 2000, 01; UPSEAT 2002] |
| A. | \[\frac{1}{2}|a-b|\] |
| B. | \[\frac{1}{2}|a+b|\] |
| C. | \[|a-b|\] |
| D. | \[|a+b|\] |
| Answer» B. \[\frac{1}{2}|a+b|\] | |
| 7412. |
If a, b and c are unit vectors such that \[\mathbf{a}+\mathbf{b}-\mathbf{c}=0,\] then the angle between a and b is [Roorkee Qualifying 1998; MP PET 1999; UPSEAT 2000; RPET 2002] |
| A. | \[\pi /6\] |
| B. | \[\pi /3\] |
| C. | \[\pi /2\] |
| D. | \[2\pi /3\] |
| Answer» E. | |
| 7413. |
If a, b, c are mutually perpendicular vectors of equal magnitudes, then the angle between the vectors a and \[\mathbf{a}+\mathbf{b}+\mathbf{c}\] is |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{6}\] |
| C. | \[{{\cos }^{-1}}\frac{1}{\sqrt{3}}\] |
| D. | \[\frac{\pi }{2}\] |
| Answer» D. \[\frac{\pi }{2}\] | |
| 7414. |
If the position vectors of the points A, B, C, D be \[\mathbf{i}+\mathbf{j}+\mathbf{k},\,\,2\,\mathbf{i}+5\,\mathbf{j},\,\,3\,\mathbf{i}+2\,\mathbf{j}-3\mathbf{k}\]and \[\mathbf{i}-6\,\mathbf{j}-\mathbf{k},\] then the angle between the vectors \[\overrightarrow{AB}\] and \[\overrightarrow{CD}\] is |
| A. | \[\frac{\pi }{4}\] |
| B. | \[\frac{\pi }{3}\] |
| C. | \[\frac{\pi }{2}\] |
| D. | \[\pi \] |
| Answer» E. | |
| 7415. |
The value of x for which the angle between the vectors \[\mathbf{a}=x\mathbf{i}-3\mathbf{j}-\mathbf{k},\,\,\mathbf{b}=2x\mathbf{i}+x\mathbf{j}-\mathbf{k}\] is acute and the angle between the vectors b and the axis of ordinate is obtuse, are |
| A. | 1, 2 |
| B. | ? 2, ? 3 |
| C. | x > 0 |
| D. | None of these |
| Answer» C. x > 0 | |
| 7416. |
If \[a\,.\,i=a\,.\,(i+j)=a\,.\,(i+j+k)\], then a = [EAMCET 2002] |
| A. | i |
| B. | k |
| C. | j |
| D. | i + j + k |
| Answer» B. k | |
| 7417. |
If \[|\mathbf{a}|\,\,=3,\,\,\,|\mathbf{b}|\,\,=1,\,\,|\mathbf{c}|\,\,=4\] and \[\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0},\] then \[\mathbf{a}\,.\,\mathbf{b}+\mathbf{b}\,.\,\mathbf{c}+\mathbf{c}\,.\,\mathbf{a}=\] [MP PET 1995; RPET 2000] |
| A. | ? 13 |
| B. | ? 10 |
| C. | 13 |
| D. | 10 |
| Answer» B. ? 10 | |
| 7418. |
If \[\overrightarrow{{{F}_{1}}}=\mathbf{i}-\mathbf{j}+\mathbf{k},\] \[\overrightarrow{{{F}_{2}}}=-\mathbf{i}+2\mathbf{j}-\mathbf{k},\] \[\overrightarrow{{{F}_{3}}}=\mathbf{j}-\mathbf{k},\] \[\vec{A}=4\mathbf{i}-3\mathbf{j}-2\mathbf{k}\] and \[\vec{B}=6\mathbf{i}+\mathbf{j}-3\mathbf{k},\] then the scalar product of \[\overrightarrow{{{F}_{1}}}+\overrightarrow{{{F}_{2}}}+\overrightarrow{{{F}_{3}}}\]and \[\overrightarrow{AB}\] will be [Roorkee 1980] |
| A. | 3 |
| B. | 6 |
| C. | 9 |
| D. | 12 |
| Answer» D. 12 | |
| 7419. |
The projection of the vector \[i-2j+k\] on the vector \[4i-4j+7k\] is [RPET 1990; MNR 1980; MP PET 2002; UPSEAT 2002; Pb. CET 2004] |
| A. | \[\frac{5\sqrt{6}}{10}\] |
| B. | \[\frac{19}{9}\] |
| C. | \[\frac{9}{19}\] |
| D. | \[\frac{\sqrt{6}}{19}\] |
| Answer» C. \[\frac{9}{19}\] | |
| 7420. |
\[(\mathbf{a}\,.\,\mathbf{i})\,\mathbf{i}+(\mathbf{a}\,.\,\mathbf{j})\mathbf{j}+(\mathbf{a}\,.\,\mathbf{k})\,\mathbf{k}=\] [Karnataka CET 2004] |
| A. | a |
| B. | 2 a |
| C. | 0 |
| D. | None of these |
| Answer» B. 2 a | |
| 7421. |
If a unit vector lies in yz?plane and makes angles of \[{{30}^{o}}\] and \[{{60}^{o}}\] with the positive y-axis and z-axis respectively, then its components along the co-ordinate axes will be |
| A. | \[\frac{\sqrt{3}}{2},\,\,\frac{1}{2},\,0\] |
| B. | \[0,\,\,\frac{\sqrt{3}}{2},\,\,\frac{1}{2}\] |
| C. | \[\frac{\sqrt{3}}{2},\,\,0,\,\,\frac{1}{2}\] |
| D. | \[0,\,\,\frac{1}{2},\,\frac{\sqrt{3}}{2}\] |
| Answer» C. \[\frac{\sqrt{3}}{2},\,\,0,\,\,\frac{1}{2}\] | |
| 7422. |
. If \[\mathbf{a}\,.\,\mathbf{b}=\mathbf{b}\,.\,\mathbf{c}=\mathbf{c}\,.\,\mathbf{a}=0\] then the value of [a b c] is equal to [Pb. CET 2000] |
| A. | 1 |
| B. | ? 1 |
| C. | \[|\mathbf{a}||\mathbf{b}||\mathbf{c}|\] |
| D. | 0 |
| Answer» D. 0 | |
| 7423. |
If the vectors \[4i+11j+mk,\,7i+2j+6k\] and \[i+5j+4k\] are coplanar, then m is [Karnataka CET 2003] |
| A. | 38 |
| B. | 0 |
| C. | 10 |
| D. | ? 10 |
| Answer» D. ? 10 | |
| 7424. |
What will be the volume of that parallelopiped whose sides are a = i ? j + k, b = i ? 3j + 4k and c = 2i ? 5j + 3k [UPSEAT 1999] |
| A. | 5 unit |
| B. | 6 unit |
| C. | 7 unit |
| D. | 8 unit |
| Answer» D. 8 unit | |
| 7425. |
If \[\mathbf{a}=3\mathbf{i}-2\mathbf{j}+2\mathbf{k},\,\,\,\mathbf{b}=6\mathbf{i}+4\mathbf{j}-2\mathbf{k}\] and \[\mathbf{c}=3\mathbf{i}-2\mathbf{j}-4\mathbf{k}\], then \[\mathbf{a}\,.\,\,(\mathbf{b}\times \mathbf{c})\] is [Karnataka CET 2001] |
| A. | 122 |
| B. | ? 144 |
| C. | 120 |
| D. | ? 120 |
| Answer» C. 120 | |
| 7426. |
\[[i\,\,k\,\,j]+[k\,\,j\,\,i]+[j\,\,k\,\,i]\] [UPSEAT 2002] |
| A. | 1 |
| B. | 3 |
| C. | ? 3 |
| D. | ? 1 |
| Answer» E. | |
| 7427. |
If three conterminous edges of a parallelopiped are represented by \[\mathbf{a}-\mathbf{b},\,\,\mathbf{b}-\mathbf{c}\] and \[\mathbf{c}-\mathbf{a}\], then its volume is [MP PET 1999; Pb. CET 2003] |
| A. | [a b c] |
| B. | 2 [a b c] |
| C. | \[\,{{[\mathbf{a}\,\,\mathbf{b}\,\,\mathbf{c}]}^{2}}\] |
| D. | 0 |
| Answer» E. | |
| 7428. |
If \[\mathbf{a}=\mathbf{i}-2\mathbf{j}+3\mathbf{k}\] and \[\mathbf{b}=3\mathbf{i}+\mathbf{j}+2\mathbf{k},\] then the unit vector perpendicular to a and b is [MP PET 1996] |
| A. | \[\frac{\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{3}}\] |
| B. | \[\frac{\mathbf{i}-\mathbf{j}+\mathbf{k}}{\sqrt{3}}\] |
| C. | \[\frac{-\mathbf{i}+\mathbf{j}+\mathbf{k}}{\sqrt{3}}\] |
| D. | \[\frac{\mathbf{i}-\mathbf{j}-\mathbf{k}}{\sqrt{3}}\] |
| Answer» D. \[\frac{\mathbf{i}-\mathbf{j}-\mathbf{k}}{\sqrt{3}}\] | |
| 7429. |
If \[\mathbf{i},\,\mathbf{j},\,\mathbf{k}\] are the unit vectors and mutually perpendicular, then \[[\mathbf{i}\,\mathbf{k}\,\mathbf{j}]\] is equal to [RPET 1986] |
| A. | 0 |
| B. | ? 1 |
| C. | 1 |
| D. | None of these |
| Answer» C. 1 | |
| 7430. |
If \[\mathbf{a}\,.\,\mathbf{i}=4,\] then \[(\mathbf{a}\times \mathbf{j})\,.\,(2\mathbf{j}-3\mathbf{k})=\] [EAMCET 1994] |
| A. | 12 |
| B. | 2 |
| C. | 0 |
| D. | ? 12 |
| Answer» E. | |
| 7431. |
If a, b, c be any three non-coplanar vectors, then \[[\mathbf{a}+\mathbf{b}\,\,\,\mathbf{b}+\mathbf{c}\,\,\,\mathbf{c}+\mathbf{a}]=\] [RPET 1988; MP PET 1990, 02; Kerala (Engg.) 2002] |
| A. | \[|\mathbf{a}\,\mathbf{b}\,\mathbf{c}|\] |
| B. | 2\[[\mathbf{a}\,\mathbf{b}\,\mathbf{c}]\] |
| C. | \[{{[\,\mathbf{a}\,\mathbf{b}\,\mathbf{c}\,]}^{2}}\] |
| D. | \[2\,{{[\,\mathbf{a}\,\mathbf{b}\,\mathbf{c}\,]}^{2}}\] |
| Answer» C. \[{{[\,\mathbf{a}\,\mathbf{b}\,\mathbf{c}\,]}^{2}}\] | |
| 7432. |
The vectors \[3\,\mathbf{i}+\mathbf{j}-5\,\mathbf{k}\] and \[a\,\mathbf{i}+b\,\mathbf{j}-15\,\mathbf{k}\]are collinear, if [RPET 1986; MP PET 1988] |
| A. | \[a=3,\,\,b=1\] |
| B. | \[a=9,\,\,b=1\] |
| C. | \[a=3,\,\,b=3\] |
| D. | \[a=9,\,\,b=3\] |
| Answer» E. | |
| 7433. |
If \[\mathbf{a}=\mathbf{i}-\mathbf{j}\] and \[\mathbf{b}=\mathbf{i}+\mathbf{k}\], then a unit vector coplanar with a and b and perpendicular to a is |
| A. | i |
| B. | j |
| C. | k |
| D. | None of these |
| Answer» E. | |
| 7434. |
If \[ABCDEF\] is regular hexagon, then \[\overrightarrow{AD}\,+\overrightarrow{EB}+\overrightarrow{FC}=\] [Karnataka CET 2002] |
| A. | 0 |
| B. | \[2\overrightarrow{AB}\] |
| C. | \[3\overrightarrow{AB}\] |
| D. | \[4\overrightarrow{AB}\] |
| Answer» E. | |
| 7435. |
Let A and B be points with position vectors a and b with respect to the origin O. If the point C on OA is such that \[2AC=CO,\,\,CD\] is parallel to OB and \[|\overrightarrow{CD}|\,\,=\,\,3|\overrightarrow{OB}|,\] then \[\overrightarrow{AD}\] is equal to |
| A. | \[3\mathbf{b}-\frac{\mathbf{a}}{2}\] |
| B. | \[3\mathbf{b}+\frac{\mathbf{a}}{2}\] |
| C. | \[3\mathbf{b}-\frac{\mathbf{a}}{3}\] |
| D. | \[3\mathbf{b}+\frac{\mathbf{a}}{3}\] |
| Answer» D. \[3\mathbf{b}+\frac{\mathbf{a}}{3}\] | |
| 7436. |
If C is the middle point of AB and P is any point outside AB, then [MNR 1991; UPSEAT 2000; AIEEE 2005] |
| A. | \[\overrightarrow{PA}+\overrightarrow{PB}=\overrightarrow{PC}\] |
| B. | \[\overrightarrow{PA}+\overrightarrow{PB}=2\,\overrightarrow{PC}\] |
| C. | \[\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC}=0\] |
| D. | \[\overrightarrow{PA}+\overrightarrow{PB}+2\,\overrightarrow{PC}=0\] |
| Answer» C. \[\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC}=0\] | |
| 7437. |
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. \[\overrightarrow{AB}\,\,\bot \,\,\overrightarrow{CD}\] | |
| 7438. |
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. | |
| 7439. |
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. \[2\,\overrightarrow{DE}\] | |
| 7440. |
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. \[\overrightarrow{AC}\,\,+\,\,\overrightarrow{AB}\,\,-\,\,\overrightarrow{AF}\] | |
| 7441. |
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. | |
| 7442. |
P is a point on the side BC of the \[\Delta \,ABC\] and Q is a point such that \[\overrightarrow{PQ}\] is the resultant of \[\overrightarrow{AP},\,\overrightarrow{PB},\,\overrightarrow{PC}.\] Then ABQC is a |
| A. | Square |
| B. | Rectangle |
| C. | Parallelogram |
| D. | Trapezium |
| Answer» D. Trapezium | |
| 7443. |
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. \[11+2\sqrt{2}\] | |
| 7444. |
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. \[m=\pm \,2\] | |
| 7445. |
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 | |
| 7446. |
If the position vectors of A and B are \[\mathbf{i}+3\mathbf{j}-7\mathbf{k}\] and \[5\mathbf{i}-2\mathbf{j}+4\mathbf{k},\] then the direction cosine of \[\overrightarrow{AB}\] along y-axis is [MNR 1989] |
| A. | \[\frac{4}{\sqrt{162}}\] |
| B. | \[-\frac{5}{\sqrt{162}}\] |
| C. | 5 |
| D. | 11 |
| Answer» C. 5 | |
| 7447. |
The magnitudes of mutually perpendicular forces a, b and c are 2, 10 and 11 respectively. Then the magnitude of its resultant is [IIT 1984] |
| A. | 12 |
| B. | 15 |
| C. | 9 |
| D. | None |
| Answer» C. 9 | |
| 7448. |
The vectors a and b are non-collinear. The value of x for which the vectors \[\mathbf{c}=(x-2)\,\mathbf{a}+\mathbf{b}\] and \[\mathbf{d}=(2x+1)\,\mathbf{a}-\mathbf{b}\] are collinear, is |
| A. | 1 |
| B. | \[\frac{1}{2}\] |
| C. | \[\frac{1}{3}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7449. |
If \[\hat{a},\,\,\hat{b}\] and \[\hat{c}\] are three unit vectors inclined to each other at an angle \[\theta \], then the maximum value of \[\theta \] is |
| A. | \[\frac{\pi }{3}\] |
| B. | \[\frac{\pi }{2}\] |
| C. | \[\frac{2\pi }{3}\] |
| D. | \[\frac{5\pi }{6}\] |
| Answer» D. \[\frac{5\pi }{6}\] | |
| 7450. |
If vectors \[\vec{a}\] and \[\vec{b}\] are two adjacent sides of a Parallelogram, then the vector representing the altitude of the parallelogram which is perpendicular to \[\vec{a}\] is |
| A. | \[\vec{b}+\frac{\vec{b}\times \vec{a}}{{{\left| {\vec{a}} \right|}^{2}}}\] |
| B. | \[\frac{\vec{a}\cdot \vec{b}}{{{\left| {\vec{b}} \right|}^{2}}}\] |
| C. | \[\vec{b}-\frac{\vec{b}\cdot \vec{a}}{{{\left| {\vec{a}} \right|}^{2}}}\vec{a}\] |
| D. | \[\frac{\vec{a}\times (\vec{b}\times \vec{a})}{{{\left| {\vec{b}} \right|}^{2}}}\] |
| Answer» D. \[\frac{\vec{a}\times (\vec{b}\times \vec{a})}{{{\left| {\vec{b}} \right|}^{2}}}\] | |