JEE (Main) Mathematics - Vector Algebra MCQs for Practice

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JEE (Main) Mathematics - VECTOR ALGEBRA MCQs

46. Which of the following is a scalar quantity?
a) Force
b) Velocity
c) Speed
d) Displacement
Answer: c) Speed

47. The sum of two vectors \( \mathbf{A} = 3\hat{i} + 4\hat{j} \) and \( \mathbf{B} = 2\hat{i} + \hat{j} \) is:
a) \( 5\hat{i} + 5\hat{j} \)
b) \( 5\hat{i} + 4\hat{j} \)
c) \( 6\hat{i} + 5\hat{j} \)
d) \( 4\hat{i} + 5\hat{j} \)
Answer: a) \( 5\hat{i} + 5\hat{j} \)

48. The unit vector in the direction of \( \mathbf{A} = 4\hat{i} + 3\hat{j} \) is:
a) \( \hat{i} + \hat{j} \)
b) \( \frac{4}{5}\hat{i} + \frac{3}{5}\hat{j} \)
c) \( \frac{3}{5}\hat{i} + \frac{4}{5}\hat{j} \)
d) \( \frac{5}{3}\hat{i} + \frac{4}{3}\hat{j} \)
Answer: b) \( \frac{4}{5}\hat{i} + \frac{3}{5}\hat{j} \)

49. The components of a vector \( \mathbf{A} = 5\hat{i} - 3\hat{j} + 2\hat{k} \) in the direction of \( \hat{i} \) and \( \hat{j} \) are:
a) \( 5\hat{i} + 3\hat{j} \)
b) \( 5\hat{i} - 3\hat{j} \)
c) \( 5\hat{i} + 2\hat{k} \)
d) \( -3\hat{j} + 2\hat{k} \)
Answer: b) \( 5\hat{i} - 3\hat{j} \)

50. If \( \mathbf{A} = 3\hat{i} + 2\hat{j} \) and \( \mathbf{B} = \hat{i} + 4\hat{j} \), the vector \( \mathbf{A} + \mathbf{B} \) is:
a) \( 4\hat{i} + 6\hat{j} \)
b) \( 2\hat{i} + 6\hat{j} \)
c) \( 4\hat{i} + 2\hat{j} \)
d) \( 2\hat{i} + 2\hat{j} \)
Answer: a) \( 4\hat{i} + 6\hat{j} \)

51. The scalar (dot) product of two vectors \( \mathbf{A} = 3\hat{i} + \hat{j} \) and \( \mathbf{B} = 2\hat{i} - 4\hat{j} \) is:
a) 6
b) 2
c) 8
d) -2
Answer: d) -2

52. The magnitude of the vector \( \mathbf{A} = 3\hat{i} + 4\hat{j} \) is:
a) 5
b) 7
c) 6
d) 10
Answer: a) 5

53. The cross product of two vectors \( \mathbf{A} = 2\hat{i} + \hat{j} + 3\hat{k} \) and \( \mathbf{B} = 4\hat{i} + 2\hat{j} + \hat{k} \) is:
a) \( -\hat{i} + 7\hat{j} + 6\hat{k} \)
b) \( -\hat{i} + 5\hat{j} + 6\hat{k} \)
c) \( 2\hat{i} - 7\hat{j} - 4\hat{k} \)
d) \( -\hat{i} - 5\hat{j} + 6\hat{k} \)
Answer: a) \( -\hat{i} + 7\hat{j} + 6\hat{k} \)

54. The angle between two vectors \( \mathbf{A} = \hat{i} + \hat{j} + \hat{k} \) and \( \mathbf{B} = 2\hat{i} + 3\hat{j} + 4\hat{k} \) is:
a) 0°
b) 45°
c) 60°
d) 90°
Answer: c) 60°

55. If the scalar product of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is zero, then the vectors are:
a) Parallel
b) Perpendicular
c) Collinear
d) None of the above
Answer: b) Perpendicular

56. The vector equation of a line passing through the origin in the direction of the vector \( \mathbf{A} = 4\hat{i} + 3\hat{j} \) is:
a) \( \mathbf{r} = 4\hat{i} + 3\hat{j} \)
b) \( \mathbf{r} = t(4\hat{i} + 3\hat{j}) \)
c) \( \mathbf{r} = t(\hat{i} + \hat{j}) \)
d) \( \mathbf{r} = 4t\hat{i} + 3t\hat{j} \)
Answer: b) \( \mathbf{r} = t(4\hat{i} + 3\hat{j}) \)

57. The component of the vector \( \mathbf{A} = 4\hat{i} + 3\hat{j} \) along the direction of the unit vector \( \hat{i} \) is:
a) 4
b) 3
c) 7
d) 2
Answer: a) 4

58. The cross product of two parallel vectors is:
a) Zero
b) A non-zero vector
c) A scalar
d) Undefined
Answer: a) Zero

59. The magnitude of the cross product of two vectors \( \mathbf{A} \) and \( \mathbf{B} \) is given by:
a) \( |\mathbf{A}||\mathbf{B}| \)
b) \( |\mathbf{A}||\mathbf{B}|\cos\theta \)
c) \( |\mathbf{A}||\mathbf{B}|\sin\theta \)
d) \( |\mathbf{A}||\mathbf{B}|/\theta \)
Answer: c) \( |\mathbf{A}||\mathbf{B}|\sin\theta \)

60. The direction ratios of a line parallel to the vector \( \mathbf{A} = 2\hat{i} - 3\hat{j} + \hat{k} \) are:
a) 2, -3, 1
b) -2, 3, -1
c) 1, -3, 2
d) -1, 3, 2
Answer: a) 2, -3, 1

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JEE (Main) Mathematics - VECTOR ALGEBRA MCQs

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