MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics Questions and Answers 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. | \(\frac{π}{3}\) |
| B. | \(\frac{π}{6}\) |
| C. | \(cos^{-1}\frac{\sqrt{2}}{3}\) |
| D. | \(cos^{-1}\frac{2}{\sqrt{3}}\) |
| Answer» C. \(cos^{-1}\frac{\sqrt{2}}{3}\) | |
| 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. | \(cos^{-1}-\frac{\sqrt{3}}{2}\) |
| B. | \(cos^{-1}-\frac{2}{\sqrt{3}}\) |
| C. | \(cos^{-1}-\sqrt{2}\) |
| D. | \(cos^{-1}-\sqrt{\frac{3}{2}}\) |
| 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. | \(cos^{-1}\sqrt{\frac{58}{3}}\) |
| B. | \(cos^{-1}\frac{\sqrt{58}}{3}\) |
| C. | \(cos^{-1}\frac{58}{3\sqrt{3}}\) |
| D. | \(cos^{-1}\frac{\sqrt{58}}{3\sqrt{3}}\) |
| 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. | \(cos^{-1}\frac{1}{\sqrt{3}}\) |
| B. | \(cos^{-1}\sqrt{3}\) |
| C. | \(cos^{-1}\frac{3}{\sqrt{2}}\) |
| D. | \(cos^{-1}\frac{2}{\sqrt{3}}\) |
| Answer» B. \(cos^{-1}\sqrt{3}\) | |
| 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 | |