Vectors · NDA previous year questions

2017 8 questions

1. Q512017 · 10 Sept 2017

   If $\alpha ,\beta$ and $\gamma$ are the angles which the vector $\overrightarrow{OP}$ ($O$ being the origin) makes with positive direction of the coordinate axes, then which of the following are correct? 1. ${\cos }^2\alpha +{\cos }^2\beta ={\sin }^2\gamma$ 2. ${\sin }^2\alpha +{\sin }^2\beta ={\cos }^2\gamma$ 3. ${\sin }^2\alpha +{\sin }^2\beta +{\sin }^2\gamma =2$ Select the correct answer using the code given below.

   1. A.1 and 2 only
   2. B.2 and 3 only
   3. C.1 and 3 only
   4. D.1, 2 and 3
   Show answer

   Answer: C

2. Q842017 · 10 Sept 2017

   Let $\vec{\alpha }=\hat{i}+2\hat{j}-\hat{k}$, $\vec{\beta }=2\hat{i}-\hat{j}+3\hat{k}$ and $\vec{\gamma }=2\hat{i}+\hat{j}+6\hat{k}$ be three vectors. If $\vec{\alpha }$ and $\vec{\beta }$ are both perpendicular to the vector $\vec{\delta }$ and $\vec{\delta }\cdot \vec{\gamma }=10$, then what is the magnitude of $\vec{\delta }$?

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

3. Q852017 · 10 Sept 2017

   If $\hat{a}$ and $\hat{b}$ are two unit vectors, then the vector $(\hat{a}+\hat{b})\times (\hat{a}\times \hat{b})$ is parallel to

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

4. Q862017 · 10 Sept 2017

   A force $\vec{F}=\hat{i}+3\hat{j}+2\hat{k}$ acts on a particle to displace it from the point $A(\hat{i}+2\hat{j}-3\hat{k})$ to the point $B(3\hat{i}-\hat{j}+5\hat{k})$. The work done by the force will be

   1. A.5 units
   2. B.7 units
   3. C.9 units
   4. D.10 units
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   Answer: C

5. Q872017 · 10 Sept 2017

   For any vector $\vec{a}$ $|\vec{a}\times \hat{i}{|}^2+|\vec{a}\times \hat{j}{|}^2+|\vec{a}\times \hat{k}{|}^2$ is equal to

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

6. Q882017 · 10 Sept 2017

   If the vectors $a\hat{i}+\hat{j}+\hat{k}$, $\hat{i}+b\hat{j}+\hat{k}$ and $\hat{i}+\hat{j}+c\hat{k}$ ($a,b,c\ne 1$) are coplanar, then the value of $\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}$ is equal to

   1. A.0
   2. B.1
   3. C.$a+b+c$
   4. D.$abc$
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   Answer: B

7. Q622017 · 23 Apr 2017

   The points $P(3,2,4)$, $Q(4,5,2)$, $R(5,8,0)$ and $S(2,-1,6)$ are

   1. A.vertices of a rhombus which is not a square
   2. B.non-coplanar
   3. C.collinear
   4. D.coplanar but not collinear
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   Answer: C

8. Q922017 · 23 Apr 2017

   If $\vec{a}=\hat{i}-\hat{j}+\hat{k}$, $\vec{b}=2\hat{i}+3\hat{j}+2\hat{k}$ and $\vec{c}=\hat{i}+m\hat{j}+n\hat{k}$ are three coplanar vectors and $|\vec{c}|=\sqrt{6}$, then which one of the following is correct?

   1. A.$m=2$ and $n=\pm 1$
   2. B.$m=\pm 2$ and $n=-1$
   3. C.$m=2$ and $n=-1$
   4. D.$m=\pm 2$ and $n=1$
   Show answer

   Answer: D