Vectors · NDA previous year questions

2015 15 questions

1. Q952015 · 27 Sept 2015

   $ABCD$ is a parallelogram and $P$ is the point of intersection of the diagonals. If $O$ is the origin, then $$\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}\text{ is equal to}$$

   1. A.$4\overrightarrow{OP}$
   2. B.$2\overrightarrow{OP}$
   3. C.$\overrightarrow{OP}$
   4. D.Null vector
   Show answer

   Answer: A

2. Q962015 · 27 Sept 2015

   If $\vec{b}$ and $\vec{c}$ are the position vectors of the points $B$ and $C$ respectively, then the position vector of the point $D$ such that $\overrightarrow{BD}=4\overrightarrow{BC}$ is

   1. A.$4(\vec{c}-\vec{b})$
   2. B.$-4(\vec{c}-\vec{b})$
   3. C.$4\vec{c}-3\vec{b}$
   4. D.$4\vec{c}+3\vec{b}$
   Show answer

   Answer: C

3. Q972015 · 27 Sept 2015

   If the position vector $\vec{a}$ of the point $(5,n)$ is such that $|\vec{a}|=13$, then the value/values of $n$ can be

   1. A.$\pm 8$
   2. B.$\pm 12$
   3. C.8 only
   4. D.12 only
   Show answer

   Answer: B

4. Q982015 · 27 Sept 2015

   If $|\vec{a}|=2$ and $|\vec{b}|=3$, then $|\vec{a}\times \vec{b}{|}^2+|\vec{a}\cdot \vec{b}{|}^2$ is equal to

   1. A.72
   2. B.64
   3. C.48
   4. D.36
   Show answer

   Answer: D

5. Q992015 · 27 Sept 2015

   Consider the following inequalities in respect of vectors $\vec{a}$ and $\vec{b}$: 1. $|\vec{a}+\vec{b}|\le |\vec{a}|+|\vec{b}|$ 2. $|\vec{a}-\vec{b}|\ge |\vec{a}|-|\vec{b}|$ Which of the above is/are correct?

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
   Show answer

   Answer: C

6. Q1002015 · 27 Sept 2015

   If the magnitude of difference of two unit vectors is $\sqrt{3}$, then the magnitude of sum of the two vectors is

   1. A.$\frac{1}{2}$ unit
   2. B.1 unit
   3. C.2 unit
   4. D.3 unit
   Show answer

   Answer: B

7. Q1012015 · 27 Sept 2015

   If the vectors $\alpha \hat{i}+\alpha \hat{j}+\gamma \hat{k},\hat{i}+\hat{k}$ and $\gamma \hat{i}+\gamma \hat{j}+\beta \hat{k}$ lie on a plane, where $\alpha ,\beta$ and $\gamma$ are distinct non-negative numbers, then $\gamma$ is

   1. A.Arithmetic mean of $\alpha$ and $\beta$
   2. B.Geometric mean of $\alpha$ and $\beta$
   3. C.Harmonic mean of $\alpha$ and $\beta$
   4. D.None of the above
   Show answer

   Answer: B

8. Q1022015 · 27 Sept 2015

   The vectors $\vec{a},\vec{b},\vec{c}$ and $\vec{d}$ are such that $\vec{a}\times \vec{b}=\vec{c}\times \vec{d}$ and $\vec{a}\times \vec{c}=\vec{b}\times \vec{d}$. Which of the following is/are correct? 1. $(\vec{a}-\vec{d})\times (\vec{b}-\vec{c})=\vec{0}$ 2. $(\vec{a}\times \vec{b})\times (\vec{c}\times \vec{d})=\vec{0}$ Select the correct answer using the code given below:

   1. A.1 only
   2. B.2 only
   3. C.Both 1 and 2
   4. D.Neither 1 nor 2
   Show answer

   Answer: C

9. Q942015 · 19 Apr 2015

   The adjacent sides $AB$ and $AC$ of a triangle $ABC$ are represented by the vectors $-2\hat{i}+3\hat{j}+2\hat{k}$ and $-4\hat{i}+5\hat{j}+2\hat{k}$ respectively. The area of the triangle $ABC$ is

   1. A.6 square units
   2. B.5 square units
   3. C.4 square units
   4. D.3 square units
   Show answer

   Answer: D

10. Q952015 · 19 Apr 2015

    A force $\vec{F}=3\hat{i}+4\hat{j}-3\hat{k}$ is applied at the point $P$, whose position vector is $\vec{r}=2\hat{i}-2\hat{j}-3\hat{k}$. What is the magnitude of the moment of the force about the origin?

    1. A.23 units
    2. B.19 units
    3. C.18 units
    4. D.21 units
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    Answer: A

11. Q962015 · 19 Apr 2015

    Given that the vectors $\vec{\alpha }$ and $\vec{\beta }$ are non-collinear. The values of $x$ and $y$ for which $\vec{u}-\vec{v}=\vec{w}$ holds true if $\vec{u}=2x\vec{\alpha }+y\vec{\beta }$, $\vec{v}=2y\vec{\alpha }+3x\vec{\beta }$ and $\vec{w}=2\vec{\alpha }-5\vec{\beta }$, are

    1. A.$x=2,y=1$
    2. B.$x=1,y=2$
    3. C.$x=-2,y=1$
    4. D.$x=-2,y=-1$
    Show answer

    Answer: A

12. Q972015 · 19 Apr 2015

    If $|\vec{a}|=7$, $|\vec{b}|=11$ and $|\vec{a}+\vec{b}|=10\sqrt{3}$, then $|\vec{a}-\vec{b}|$ is equal to

    1. A.40
    2. B.10
    3. C.$4\sqrt{10}$
    4. D.$2\sqrt{10}$
    Show answer

    Answer: D

13. Q982015 · 19 Apr 2015

    Let $\alpha ,\beta ,\gamma$ be distinct real numbers. The points with position vectors $\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}$, $\beta \hat{i}+\gamma \hat{j}+\alpha \hat{k}$ and $\gamma \hat{i}+\alpha \hat{j}+\beta \hat{k}$

    1. A.are collinear
    2. B.form an equilateral triangle
    3. C.form a scalene triangle
    4. D.form a right-angled triangle
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    Answer: B

14. Q992015 · 19 Apr 2015

    If $\vec{a}+\vec{b}+\vec{c}=\vec{0}$, then which of the following is/are correct? 1. $\vec{a},\vec{b},\vec{c}$ are coplanar. 2. $\vec{a}\times \vec{b}=\vec{b}\times \vec{c}=\vec{c}\times \vec{a}$ Select the correct answer using the code given below.

    1. A.1 only
    2. B.2 only
    3. C.Both 1 and 2
    4. D.Neither 1 nor 2
    Show answer

    Answer: C

15. Q1002015 · 19 Apr 2015

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

    1. A.$\vec{a}=\lambda \vec{b}$ for some scalar $\lambda$
    2. B.$\vec{a}$ is parallel to $\vec{b}$
    3. C.$\vec{a}$ is perpendicular to $\vec{b}$
    4. D.$\vec{a}=\vec{b}=\vec{0}$
    Show answer

    Answer: C