Vectors · NDA previous year questions

2009 15 questions

1. Q662009 · 30 Aug 2009

   If $\hat{a}$ and $\hat{b}$ are the unit vectors along $\bar{a}$ and $\bar{b}$ respectively, then what is the projection of $\bar{b}$ on $\bar{a}$ ?

   1. A.$\bar{a}\bullet \bar{b}$
   2. B.$\hat{a}\bullet \hat{b}$
   3. C.$\hat{a}\bullet \bar{b}$
   4. D.$|\bar{a}\times \bar{b}|$
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   Answer: C

2. Q672009 · 30 Aug 2009

   What are the unit vectors parallel to xy-plane and perpendicular to the vector $4\hat{i}-3\hat{j}+\hat{k}$ ?

   1. A.$\pm (3\hat{i}+4\hat{j})/5$
   2. B.$\pm (4\hat{i}+3\hat{j})/5$
   3. C.$\pm (3\hat{i}-4\hat{j})/5$
   4. D.$\pm (4\hat{i}-3\hat{j})/5$
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   Answer: A

3. Q682009 · 30 Aug 2009

   What is the vector in the $xy$-plane through origin and perpendicular to the vector $\bar{r}=a\hat{i}+b\hat{j}$ and of the same length ?

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

4. Q692009 · 30 Aug 2009

   Given $\bar{a}=2\hat{i}-3\hat{j}+4\hat{k}$ and $\bar{b}$ is a unit vector co-directional with $\bar{a}$. If $m$ is a scalar such that $\hat{b}=m\bar{a}$, then what is the value of $m$ ?

   1. A.$1/5$
   2. B.$1/\sqrt{5}$
   3. C.$1/29$
   4. D.$1/\sqrt{29}$
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   Answer: D

5. Q702009 · 30 Aug 2009

   The magnitude of the vectors $\bar{a}$ and $\bar{b}$ are equal and the angle between them is $60^{\circ }$. If the vectors $\lambda \bar{a}+\bar{b}$ and $\bar{a}-\lambda \bar{b}$ are perpendicular to each other, then what is the value of $\lambda$ ?

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

6. Q712009 · 30 Aug 2009

   If $|\bar{a}|=3$, $|\bar{b}|=4$ and $|\bar{a}-\bar{b}|=7$, then what is the value of $|\bar{a}+\bar{b}|$ ?

   1. A.3
   2. B.2
   3. C.1
   4. D.0
   Show answer

   Answer: C

7. Q722009 · 30 Aug 2009

   Consider the diagonals of a quadrilateral formed by the vectors $3\hat{i}+6\hat{j}-2\hat{k}$ and $4\hat{i}-\hat{j}+3\hat{k}$. The quadrilateral must be a :

   1. A.Square
   2. B.Rhombus
   3. C.Rectangle
   4. D.None of the above
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   Answer: B

8. Q732009 · 30 Aug 2009

   If $p=\sin (989^{\circ })\cos (991^{\circ })$, then which one of the following is correct ?

   1. A.$p$ is finite and positive
   2. B.$p$ is finite and negative
   3. C.$p=0$
   4. D.$p$ is undefined
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   Answer: B

9. Q742009 · 30 Aug 2009

   If $A=\frac{41\pi }{12}$, then what is the value of $\frac{1-3{\tan }^{2}A}{3\tan A-{\tan }^{3}A}$ ?

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

   Answer: B

10. Q962009 · 19 Apr 2009

    Which one of the following vectors of magnitude $\sqrt{51}$ makes equal angles with three vectors $\vec{a}=\frac{\hat{i}-2\hat{j}+2\hat{k}}{3}$, $\vec{b}=\frac{-4\hat{i}-3\hat{k}}{5}$ and $\vec{c}=\hat{j}$?

    1. A.$5\hat{i}-\hat{j}-5\hat{k}$
    2. B.$5\hat{i}+\hat{j}+5\hat{k}$
    3. C.$-5\hat{i}-\hat{j}+5\hat{k}$
    4. D.$5\hat{i}+5\hat{j}-\hat{k}$
    Show answer

    Answer: A

11. Q972009 · 19 Apr 2009

    If $|\vec{a}|=2$, $|\vec{b}|=5$ and $|\vec{a}\times \vec{b}|=8$, then what is the value of $\vec{a}\cdot \vec{b}$?

    1. A.4
    2. B.6
    3. C.8
    4. D.10
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    Answer: B

12. Q982009 · 19 Apr 2009

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

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

13. Q992009 · 19 Apr 2009

    If $\vec{a}=\hat{i}-2\hat{j}+5\hat{k}$, $\vec{b}=2\hat{i}+\hat{j}-3\hat{k}$, then what is $(\vec{b}-\vec{a})\cdot (3\vec{a}+\vec{b})$ equal to?

    1. A.106
    2. B.$-106$
    3. C.53
    4. D.$-53$
    Show answer

    Answer: B

14. Q1002009 · 19 Apr 2009

    Let $\vec{a},\vec{b},\vec{c}$ be the position vectors of points $A,B,C$ respectively. Under which one of the following conditions are the points $A,B,C$ collinear?

    1. A.$\vec{a}\times \vec{b}=\vec{0}$
    2. B.$\vec{b}\times \vec{c}$ is parallel to $\vec{a}\times \vec{b}$
    3. C.$\vec{a}\times \vec{b}$ is perpendicular to $\vec{b}\times \vec{c}$
    4. D.$(\vec{a}\times \vec{b})+(\vec{b}\times \vec{c})+(\vec{c}\times \vec{a})=\vec{0}$
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    Answer: D

15. Q1012009 · 19 Apr 2009

    If $\vec{a}=\hat{i}+\hat{j}+\hat{k},\vec{b}=\hat{i}-\hat{j}+\hat{k}$ and $\vec{c}=\hat{i}+\hat{j}-\hat{k}$, then what is $\vec{a}\times (\vec{b}+\vec{c})+\vec{b}\times (\vec{c}+\vec{a})+\vec{c}\times (\vec{a}+\vec{b})$ equal to?

    1. A.$2\hat{i}+3\hat{j}-\hat{k}$
    2. B.$2\hat{i}-3\hat{j}-\hat{k}$
    3. C.$3\hat{i}+\hat{j}+\hat{k}$
    4. D.$\vec{0}$
    Show answer

    Answer: D