MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Find the projection of vector ( vec{b}=2 hat{i}+2 sqrt{2} , hat{j}-2 hat{k} ) on the vector ( vec{a}= hat{i}- hat{j}- sqrt{2} , hat{k} ). |
| A. | 2 |
| B. | ( sqrt{2} ) |
| C. | 1 |
| D. | (2 sqrt{2} ) |
| Answer» C. 1 | |
| 2. |
Find the scalar product of the vectors ( vec{a}=6 hat{i}-7 hat{j}+5 hat{k} ,and , vec{b}=6 hat{i}-7 hat{k} ) |
| A. | 1 |
| B. | 8 |
| C. | 6 |
| D. | 3 |
| Answer» B. 8 | |
| 3. |
Find the angle between the two vectors ( vec{a} ,and , vec{b} ) with magnitude 2 and ( sqrt{3} ) respectively and ( vec{a.} , vec{b} )=4. |
| A. | ( frac{ }{3} ) |
| B. | ( frac{ }{6} ) |
| C. | (cos^{-1} u2061 frac{ sqrt{2}}{3} ) |
| D. | (cos^{-1} u2061 frac{2}{ sqrt{3}} ) |
| Answer» C. (cos^{-1} u2061 frac{ sqrt{2}}{3} ) | |
| 4. |
If two non-zero vectors ( vec{a} ,and , vec{b} ) are perpendicular to each other then their scalar product is zero. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 5. |
Find the angle between the vectors ( vec{a}=- hat{i}+ hat{j}- hat{k} ) and ( vec{b}= hat{i}- hat{j} ) |
| A. | (cos^{-1} u2061- frac{ sqrt{3}}{2} ) |
| B. | (cos^{-1} u2061- frac{2}{ sqrt{3}} ) |
| C. | (cos^{-1} u2061- sqrt{2} ) |
| D. | (cos^{-1} u2061- sqrt{ frac{3}{2}} ) |
| Answer» E. | |
| 6. |
Find the angle between the vectors ( vec{a}= hat{i}- hat{j}+2 hat{k} ,and , vec{b}=3 hat{i}+2 hat{j}+4 hat{k} ). |
| A. | (cos^{-1} u2061 sqrt{ frac{58}{3}} ) |
| B. | (cos^{-1} u2061 frac{ sqrt{58}}{3} ) |
| C. | (cos^{-1} frac{ u206158}{3 sqrt{3}} ) |
| D. | (cos^{-1} u2061 frac{ sqrt{58}}{3 sqrt{3}} ) |
| Answer» E. | |
| 7. |
Find (| vec{a}+ vec{b}| ), if (| vec{a}|=3 ,and ,| vec{b}|=4 ,and , vec{a}. vec{b}=6 ). |
| A. | 34 |
| B. | ( sqrt{37} ) |
| C. | 13 |
| D. | ( sqrt{23} ) |
| Answer» C. 13 | |
| 8. |
Find the projection of vector ( vec{a}=8 hat{i}- hat{j}+6 hat{k} ) on vector ( vec{b}= 4 hat{i}+3 hat{j} ). |
| A. | ( sqrt{ frac{29}{5}} ) |
| B. | ( frac{29}{ sqrt{5}} ) |
| C. | ( frac{ sqrt{29}}{5} ) |
| D. | ( frac{29}{5} ) |
| Answer» E. | |
| 9. |
Find the angle between the two vectors ( vec{a} ) and ( vec{b} ) with magnitude ( sqrt{3} ) and ( sqrt{2} ) respectively and ( vec{a.} , vec{b}=3 sqrt{2} ). |
| A. | (cos^{-1} u2061 frac{1}{ sqrt{3}} ) |
| B. | (cos^{-1} u2061 sqrt{3} ) |
| C. | (cos^{-1} u2061 frac{3}{ sqrt{2}} ) |
| D. | (cos^{-1} u2061 frac{2}{ sqrt{3}} ) |
| Answer» B. (cos^{-1} u2061 sqrt{3} ) | |
| 10. |
Find the scalar product of the vectors ( vec{a}=2 hat{i}+5 hat{j} ) and ( vec{b}=6 hat{i}-7 hat{j} ). |
| A. | -32 |
| B. | -23 |
| C. | 32 |
| D. | 23 |
| Answer» C. 32 | |