Vectors · NDA previous year questions

2014 14 questions

1. Q892014 · 28 Sept 2014

   If $|\vec{a}+\vec{b}|=|\vec{a}-\vec{b}|$, then which one of the following is correct?

   1. A.$|\vec{a}|=|\vec{b}|$.
   2. B.$\vec{a}$ is parallel to $\vec{b}$.
   3. C.$\vec{a}$ is perpendicular to $\vec{b}$.
   4. D.$\vec{a}$ is a unit vector.
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   Answer: C

2. Q912014 · 28 Sept 2014

   Which one of the following is the unit vector perpendicular to both $\vec{a}=-\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$?

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

3. Q922014 · 28 Sept 2014

   What is the interior acute angle of the parallelogram whose sides are represented by the vectors $\frac{1}{\sqrt{2}}\hat{i}+\frac{1}{\sqrt{2}}\hat{j}+\hat{k}$ and $\frac{1}{\sqrt{2}}\hat{i}-\frac{1}{\sqrt{2}}\hat{j}+\hat{k}$?

   1. A.$60^{\circ }$
   2. B.$45^{\circ }$
   3. C.$30^{\circ }$
   4. D.$15^{\circ }$
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   Answer: A

4. Q932014 · 28 Sept 2014

   For what value of $\lambda$ are the vectors $\lambda \hat{i}+(1+\lambda )\hat{j}+(1+2\lambda )\hat{k}$ and $(1-\lambda )\hat{i}+\lambda \hat{j}+2\hat{k}$ perpendicular?

   1. A.-1/3
   2. B.1/3
   3. C.2/3
   4. D.1
   Show answer

   Answer: A

5. Q942014 · 28 Sept 2014

   For the next four (04) items that follow: $\vec{a}+\vec{b}+\vec{c}=\vec{0}$ such that $|\vec{a}|=3$, $|\vec{b}|=5$ and $|\vec{c}|=7$. What is the angle between $\vec{a}$ and $\vec{b}$?

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

   Answer: C

6. Q952014 · 28 Sept 2014

   For the next four (04) items that follow: $\vec{a}+\vec{b}+\vec{c}=\vec{0}$ such that $|\vec{a}|=3$, $|\vec{b}|=5$ and $|\vec{c}|=7$. What is $\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a}$ equal to?

   1. A.-83
   2. B.-83/2
   3. C.75
   4. D.-75/2
   Show answer

   Answer: B

7. Q962014 · 28 Sept 2014

   For the next four (04) items that follow: $\vec{a}+\vec{b}+\vec{c}=\vec{0}$ such that $|\vec{a}|=3$, $|\vec{b}|=5$ and $|\vec{c}|=7$. What is cosine of the angle between $\vec{b}$ and $\vec{c}$?

   1. A.11/12
   2. B.13/14
   3. C.-11/12
   4. D.-13/14
   Show answer

   Answer: D

8. Q972014 · 28 Sept 2014

   For the next four (04) items that follow: $\vec{a}+\vec{b}+\vec{c}=\vec{0}$ such that $|\vec{a}|=3$, $|\vec{b}|=5$ and $|\vec{c}|=7$. What is $|\vec{a}+\vec{b}|$ equal to?

   1. A.7
   2. B.8
   3. C.10
   4. D.11
   Show answer

   Answer: A

9. Q862014 · 20 Apr 2014

   For the next two (02) items that follow: Consider the vectors $\vec{a}=\hat{i}-2\hat{j}+\hat{k}$ and $\vec{b}=4\hat{i}-4\hat{j}+7\hat{k}$. What is the scalar projection of $\vec{a}$ on $\vec{b}$?

   1. A.1
   2. B.19/9
   3. C.17/9
   4. D.23/9
   Show answer

   Answer: B

10. Q872014 · 20 Apr 2014

    For the next two (02) items that follow: Consider the vectors $\vec{a}=\hat{i}-2\hat{j}+\hat{k}$ and $\vec{b}=4\hat{i}-4\hat{j}+7\hat{k}$. What is the vector perpendicular to both the vectors?

    1. A.$-10\hat{i}-3\hat{j}+4\hat{k}$
    2. B.$-10\hat{i}+3\hat{j}+4\hat{k}$
    3. C.$10\hat{i}-3\hat{j}+4\hat{k}$
    4. D.None of the above
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    Answer: A

11. Q882014 · 20 Apr 2014

    For the next two (02) items that follow: Let $|\bar{a}|=7$, $|\bar{b}|=11$, $|\bar{a}+\bar{b}|=10\sqrt{3}$ What is $|\bar{a}-\bar{b}|$ equal to?

    1. A.$2\sqrt{2}$
    2. B.$2\sqrt{10}$
    3. C.5
    4. D.10
    Show answer

    Answer: B

12. Q892014 · 20 Apr 2014

    For the next two (02) items that follow: Let $|\bar{a}|=7$, $|\bar{b}|=11$, $|\bar{a}+\bar{b}|=10\sqrt{3}$ What is the angle between $(\bar{a}+\bar{b})$ and $(\bar{a}-\bar{b})$?

    1. A.$\frac{\pi }{2}$
    2. B.$\frac{\pi }{3}$
    3. C.$\frac{\pi }{6}$
    4. D.None of the above
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    Answer: D

13. Q1182014 · 20 Apr 2014

    For the next two (02) items that follow: Let a vector $\bar{r}$ make angles $60^{\circ }$, $30^{\circ }$ with x and y-axes respectively. What angle does $\bar{r}$ make with z-axis?

    1. A.$30^{\circ }$
    2. B.$60^{\circ }$
    3. C.$90^{\circ }$
    4. D.$120^{\circ }$
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    Answer: C

14. Q1192014 · 20 Apr 2014

    For the next two (02) items that follow: Let a vector $\bar{r}$ make angles $60^{\circ }$, $30^{\circ }$ with x and y-axes respectively. What are the direction cosines of $\bar{r}$?

    1. A.$⟨\frac{1}{2},\frac{\sqrt{3}}{2},0⟩$
    2. B.$⟨\frac{1}{2},-\frac{\sqrt{3}}{2},0⟩$
    3. C.$⟨\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}},0⟩$
    4. D.$⟨-\frac{1}{2},\frac{\sqrt{3}}{2},0⟩$
    Show answer

    Answer: A