Vectors · NDA previous year questions

2016 7 questions

1. Q932016 · 18 Sept 2016

   Consider the following for the next two (02) items that follow: Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be three vectors such that $\vec{a}+\vec{b}+\vec{c}=\vec{0}$, and $|\vec{a}|=10$, $|\vec{b}|=6$ and $|\vec{c}|=14$. What is $\vec{a}\cdot \vec{b}+\vec{b}\cdot \vec{c}+\vec{c}\cdot \vec{a}$ equal to?

   1. A.$-332$
   2. B.$-166$
   3. C.0
   4. D.166
   Show answer

   Answer: B

2. Q942016 · 18 Sept 2016

   Consider the following for the next two (02) items that follow: Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be three vectors such that $\vec{a}+\vec{b}+\vec{c}=\vec{0}$, and $|\vec{a}|=10$, $|\vec{b}|=6$ and $|\vec{c}|=14$. What is the angle between $\vec{a}$ and $\vec{b}$?

   1. A.$30^{\circ }$
   2. B.$45^{\circ }$
   3. C.$60^{\circ }$
   4. D.$75^{\circ }$
   Show answer

   Answer: C

3. Q812016 · 17 Apr 2016

   What is a vector of unit length orthogonal to both the vectors $\hat{i}+\hat{j}+\hat{k}$ and $2\hat{i}+3\hat{j}-\hat{k}$?

   1. A.$\frac{-4\hat{i}+3\hat{j}-\hat{k}}{\sqrt{26}}$
   2. B.$\frac{-4\hat{i}+3\hat{j}+\hat{k}}{\sqrt{26}}$
   3. C.$\frac{-3\hat{i}+2\hat{j}-\hat{k}}{\sqrt{14}}$
   4. D.$\frac{-3\hat{i}+2\hat{j}+\hat{k}}{\sqrt{14}}$
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   Answer: B

4. Q822016 · 17 Apr 2016

   If $\vec{a},\vec{b}$ and $\vec{c}$ are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then which one of the following is correct?

   1. A.$\vec{a}+\vec{b}+\vec{c}=\vec{0}$
   2. B.$\vec{a}+\vec{b}+\vec{c}=\text{unit vector}$
   3. C.$\vec{a}+\vec{b}=\vec{c}$
   4. D.$\vec{a}=\vec{b}+\vec{c}$
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   Answer: A

5. Q832016 · 17 Apr 2016

   What is the area of the parallelogram having diagonals $3\hat{i}+\hat{j}-2\hat{k}$ and $\hat{i}-3\hat{j}+4\hat{k}$?

   1. A.$5\sqrt{5}$ square units
   2. B.$4\sqrt{5}$ square units
   3. C.$5\sqrt{3}$ square units
   4. D.$15\sqrt{2}$ square units
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   Answer: C

6. Q842016 · 17 Apr 2016

   For the next two (2) items that follow: Let $\hat{a},\hat{b}$ be two unit vectors and $\theta$ be the angle between them. What is $\cos \left(\frac{\theta }{2}\right)$ equal to?

   1. A.$\frac{|\hat{a}-\hat{b}|}{2}$
   2. B.$\frac{|\hat{a}+\hat{b}|}{2}$
   3. C.$\frac{|\hat{a}-\hat{b}|}{4}$
   4. D.$\frac{|\hat{a}+\hat{b}|}{4}$
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   Answer: B

7. Q852016 · 17 Apr 2016

   For the next two (2) items that follow: Let $\hat{a},\hat{b}$ be two unit vectors and $\theta$ be the angle between them. What is $\sin \left(\frac{\theta }{2}\right)$ equal to?

   1. A.$\frac{|\hat{a}-\hat{b}|}{2}$
   2. B.$\frac{|\hat{a}+\hat{b}|}{2}$
   3. C.$\frac{|\hat{a}-\hat{b}|}{4}$
   4. D.$\frac{|\hat{a}+\hat{b}|}{4}$
   Show answer

   Answer: A