Vectors · NDA previous year questions

2018 10 questions

1. Q872018 · 9 Sept 2018

   A unit vector perpendicular to each of the vectors $2\hat{i}-\hat{j}+\hat{k}$ and $3\hat{i}-4\hat{j}-\hat{k}$ is

   1. A.$\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}-\frac{1}{\sqrt{3}}\hat{k}$
   2. B.$\frac{1}{\sqrt{2}}\hat{i}+\frac{1}{2}\hat{j}+\frac{1}{2}\hat{k}$
   3. C.$\frac{1}{\sqrt{3}}\hat{i}-\frac{1}{\sqrt{3}}\hat{j}-\frac{1}{\sqrt{3}}\hat{k}$
   4. D.$\frac{1}{\sqrt{3}}\hat{i}+\frac{1}{\sqrt{3}}\hat{j}+\frac{1}{\sqrt{3}}\hat{k}$
   Show answer

   Answer: A

2. Q882018 · 9 Sept 2018

   If $|\vec{a}|=3,|\vec{b}|=4$ and $|\vec{a}-\vec{b}|=5$, then what is the value of $|\vec{a}+\vec{b}|$?

   1. A.$8$
   2. B.$6$
   3. C.$5\sqrt{2}$
   4. D.$5$
   Show answer

   Answer: D

3. Q892018 · 9 Sept 2018

   Let $\vec{a},\vec{b}$ and $\vec{c}$ be three mutually perpendicular vectors each of unit magnitude. If $\vec{A}=\vec{a}+\vec{b}+\vec{c},\vec{B}=\vec{a}-\vec{b}+\vec{c}$ and $\vec{C}=\vec{a}-\vec{b}-\vec{c}$, then which one of the following is correct?

   1. A.$|\vec{A}|>|\vec{B}|>|\vec{C}|$
   2. B.$|\vec{A}|=|\vec{B}|\ne |\vec{C}|$
   3. C.$|\vec{A}|=|\vec{B}|=|\vec{C}|$
   4. D.$|\vec{A}|\ne |\vec{B}|\ne |\vec{C}|$
   Show answer

   Answer: C

4. Q902018 · 9 Sept 2018

   What is $(\vec{a}-\vec{b})\times (\vec{a}+\vec{b})$ equal to?

   1. A.$\vec{0}$
   2. B.$\vec{a}\times \vec{b}$
   3. C.$2(\vec{a}\times \vec{b})$
   4. D.$|\vec{a}{|}^2-|\vec{b}{|}^2$
   Show answer

   Answer: C

5. Q912018 · 9 Sept 2018

   A spacecraft located at $\hat{i}+2\hat{j}+3\hat{k}$ is subjected to a force $\lambda \hat{k}$ by firing a rocket. The spacecraft is subjected to a moment of magnitude

   1. A.$\lambda$
   2. B.$\sqrt{3}\lambda$
   3. C.$\sqrt{5}\lambda$
   4. D.None of the above
   Show answer

   Answer: C

6. Q882018 · 22 Apr 2018

   If $\vec{a}$ and $\vec{b}$ are vectors such that $|\vec{a}|=2,|\vec{b}|=7$ and $\vec{a}\times \vec{b}=3\hat{i}+2\hat{j}+6\hat{k}$, then what is the acute angle between $\vec{a}$ and $\vec{b}$?

   1. A.$30^{\circ }$
   2. B.$45^{\circ }$
   3. C.$60^{\circ }$
   4. D.$90^{\circ }$
   Show answer

   Answer: A

7. Q892018 · 22 Apr 2018

   Let $\vec{p}$ and $\vec{q}$ be the position vectors of the points P and Q respectively with respect to origin O. The points R and S divide PQ internally and externally respectively in the ratio 2 : 3. If $\overrightarrow{OR}$ and $\overrightarrow{OS}$ are perpendicular, then which one of the following is correct?

   1. A.$9p^2=4q^2$
   2. B.$4p^2=9q^2$
   3. C.$9p=4q$
   4. D.$4p=9q$
   Show answer

   Answer: A

8. Q902018 · 22 Apr 2018

   What is the moment about the point $\hat{i}+2\hat{j}-\hat{k}$ of a force represented by $3\hat{i}+\hat{k}$ acting through the point $2\hat{i}-\hat{j}+3\hat{k}$?

   1. A.$-3\hat{i}+11\hat{j}+9\hat{k}$
   2. B.$3\hat{i}+2\hat{j}+9\hat{k}$
   3. C.$3\hat{i}+4\hat{j}+9\hat{k}$
   4. D.$\hat{i}+\hat{j}+\hat{k}$
   Show answer

   Answer: A

9. Q912018 · 22 Apr 2018

   If $\vec{a}+2\vec{b}+3\vec{c}=\vec{0}$ and $\vec{a}\times \vec{b}+\vec{b}\times \vec{c}+\vec{c}\times \vec{a}=\lambda (\vec{b}\times \vec{c})$, then what is the value of $\lambda$?

   1. A.$2$
   2. B.$3$
   3. C.$4$
   4. D.$6$
   Show answer

   Answer: D

10. Q922018 · 22 Apr 2018

    If the vectors $\vec{k}$ and $\vec{A}$ are parallel to each other, then what is $k\vec{k}\times \vec{A}$ equal to?

    1. A.$k^2\vec{A}$
    2. B.$\vec{0}$
    3. C.$-k^2\vec{A}$
    4. D.$\vec{A}$
    Show answer

    Answer: B