Vectors · NDA previous year questions

2019 7 questions

1. Q952019 · 17 Nov 2019

   If $\vec{a}$ and $\vec{b}$ are unit vectors and $\theta$ is the angle between them, then what is ${\sin }^2\left(\frac{\theta }{2}\right)$ equal to?

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

2. Q962019 · 17 Nov 2019

   Consider the following equations for two vectors $\vec{a}$ and $\vec{b}$: 1. $(\vec{a}+\vec{b})\cdot (\vec{a}-\vec{b})=|\vec{a}{|}^2-|\vec{b}{|}^2$ 2. $(|\vec{a}+\vec{b}|)(|\vec{a}-\vec{b}|)=|\vec{a}{|}^2-|\vec{b}{|}^2$ 3. $|\vec{a}\cdot \vec{b}{|}^2+|\vec{a}\times \vec{b}{|}^2=|\vec{a}{|}^2|\vec{b}{|}^2$ Which of the above statements are correct?

   1. A.1, 2 and 3
   2. B.1 and 2 only
   3. C.1 and 3 only
   4. D.2 and 3 only
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   Answer: C

3. Q972019 · 17 Nov 2019

   If the magnitude of the sum of two non-zero vectors is equal to the magnitude of their difference, then which one of the following is correct?

   1. A.The vectors are parallel
   2. B.The vectors are perpendicular
   3. C.The vectors are anti-parallel
   4. D.The vectors must be unit vectors
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   Answer: B

4. Q982019 · 17 Nov 2019

   What is the scalar projection of $\vec{a}=\hat{i}-2\hat{j}+\hat{k}$ on $\vec{b}=4\hat{i}-4\hat{j}+7\hat{k}$?

   1. A.$\frac{\sqrt{6}}{9}$
   2. B.$\frac{19}{9}$
   3. C.$\frac{9}{19}$
   4. D.$\frac{\sqrt{6}}{19}$
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   Answer: B

5. Q942019 · 21 Apr 2019

   If the position vectors of points A and B are $3\hat{i}-2\hat{j}+\hat{k}$ and $2\hat{i}+4\hat{j}-3\hat{k}$ respectively, then what is the length of $\overrightarrow{AB}$?

   1. A.$\sqrt{14}$
   2. B.$\sqrt{29}$
   3. C.$\sqrt{43}$
   4. D.$\sqrt{53}$
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   Answer: D

6. Q962019 · 21 Apr 2019

   The sine of the angle between vectors $\vec{a}=2\hat{i}-6\hat{j}-3\hat{k}$ and $\vec{b}=4\hat{i}+3\hat{j}-\hat{k}$ is

   1. A.$\frac{1}{\sqrt{26}}$
   2. B.$\frac{5}{\sqrt{26}}$
   3. C.$\frac{5}{26}$
   4. D.$\frac{1}{26}$
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   Answer: B

7. Q972019 · 21 Apr 2019

   What is the value of $\lambda$ for which the vectors $3\hat{i}+4\hat{j}-\hat{k}$ and $-2\hat{i}+\lambda \hat{j}+10\hat{k}$ are perpendicular ?

   1. A.1
   2. B.2
   3. C.3
   4. D.4
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   Answer: D