Vectors · NDA previous year questions

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2012 14 questions

Q912012 · 19 Aug 2012
EFGH is a rhombus such that the angle EFG is $6 0^{\circ}$ . The magnitude of vectors $F H$ and ${m E G}$ are equal where m is a scalar. What is the value of m?
1. A.3
2. B.1.5
3. C. $2$
4. D. $3$
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Answer: D
Q922012 · 19 Aug 2012
If $a \cdot b = 0$ and $a \times b = 0$ then which one of the following is correct?
1. A. $a$ is parallel to $b$
2. B. $a$ is perpendicular to $b$
3. C. $a = 0$ or $b = 0$
4. D.None of the above
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Answer: C
Q932012 · 19 Aug 2012
The vector $a \times (b \times a)$ is coplanar with:
1. A. $a$ only
2. B. $b$ only
3. C.Both $a$ and $b$
4. D.Neither $a$ nor $b$
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Answer: C
Q942012 · 19 Aug 2012
Consider the following: 1. $4 \hat{i} \times 3 \hat{i} = 0$ 2. $\frac{4 i ^}{3 i ^} = \frac{4}{3}$ 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
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Answer: A
Q952012 · 19 Aug 2012
What is the value of $λ$ for which $(λ \hat{i} + \hat{j} - \hat{k}) \times (3 \hat{i} - 2 \hat{j} + 4 \hat{k}) = (2 \hat{i} - 11 \hat{j} - 7 \hat{k})$ ?
1. A.2
2. B. $- 2$
3. C.1
4. D.7
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Answer: A
Q962012 · 19 Aug 2012
The magnitude of the scalar p for which the vector $p (- 3 \hat{i} - 2 \hat{j} + 13 \hat{k})$ is of unit length is:
1. A.1/8
2. B.1/64
3. C. $182$
4. D. $1/ 182$
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Answer: D
Q972012 · 19 Aug 2012
The vector $2 \hat{j} - \hat{k}$ lies:
1. A.in the plane of XY
2. B.in the plane of YZ
3. C.in the plane of XZ
4. D.along the X-axis
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Answer: B
Q982012 · 19 Aug 2012
ABCD is a parallelogram. If $A B = a$ , $B C = b$ , then what is $B D$ equal to?
1. A. $a + b$
2. B. $a - b$
3. C. $- a - b$
4. D. $- a + b$
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Answer: D
Q912012 · 15 Apr 2012
If $a = (2, 1, - 1), b = (1, - 1, 0), c = (5, - 1, 1)$ , then what is the unit vector parallel to $a + b - c$ in the opposite direction ?
1. A. $\frac{i ^ + j ^ - 2 k ^}{3}$
2. B. $\frac{i ^ - 2 j ^ + 2 k ^}{3}$
3. C. $\frac{2 i ^ - j ^ + 2 k ^}{3}$
4. D.None of the above
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Answer: C
Q922012 · 15 Apr 2012
If the magnitudes of two vectors $a$ and $b$ are equal then which one of the following is correct ?
1. A. $(a + b)$ is parallel to $(a - b)$
2. B. $(a + b) \cdot (a - b) = 1$
3. C. $(a + b)$ is perpendicular to $(a - b)$
4. D.None of the above
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Answer: C
Q972012 · 15 Apr 2012
What is the value of m if the vectors $2 \hat{i} - \hat{j} + \hat{k}, \hat{i} + 2 \hat{j} - 3 \hat{k}$ and $3 \hat{i} + m \hat{j} + 5 \hat{k}$ are coplanar ?
1. A.-2
2. B.2
3. C.-4
4. D.4
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Answer: C
Q982012 · 15 Apr 2012
If $∣ a ∣ = 10, ∣ b ∣ = 2$ and $a ∙ b = 12$ , then what is the value of $∣ a \times b ∣$ ?
1. A.12
2. B.16
3. C.20
4. D.24
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Answer: B
Q992012 · 15 Apr 2012
If the vectors $\hat{i} - x \hat{j} - y \hat{k}$ and $\hat{i} + x \hat{j} + y \hat{k}$ are orthogonal to each other, then what is the locus of the point (x, y)?
1. A.a parabola
2. B.an ellipse
3. C.a circle
4. D.a straight line
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Answer: C
Q1102012 · 15 Apr 2012
What is the area of the rectangle having vertices A, B, C and D with position vectors $- \hat{i} + \frac{1}{2} \hat{j} + 4 \hat{k}$ , $\hat{i} + \frac{1}{2} \hat{j} + 4 \hat{k}$ , $\hat{i} - \frac{1}{2} \hat{j} + 4 \hat{k}$ and $- \hat{i} - \frac{1}{2} \hat{j} + 4 \hat{k}$ ?
1. A.1/2 square unit
2. B.1 square unit
3. C.2 square unit
4. D.4 square unit
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Answer: C