CUET Mathematics MCQs Vectors

Question. Which of the following represents equal vectors?
a) b, c
b) m, d
c) b, d
d) a, c

Answer : C

Question. If a, b, c are three non-coplanar vectors, then (a + b + c).[(a + b) × (a + c)] is
a) [abc]
b) 0
c) 2[abc]
d) -[abc]

Answer : D

Question. The distance of the point (- 3, 4, 5) from the origin
(a) 50
(b) 5√2
(c) 6
(d) None of these
a) b
b) a
c) c
d) d

Answer : A

Question. The summation of two unit vectors is a third unit vector, then the modulus of the difference of the unit vector is
() √3
() 1 - √3
() 1 + √3
() - √3
a) c
b) d
c) b
d) a

Answer : D

Question. If a, b, c are unit vectors, then (a - b)² - (b - c)² - (c - a)²
a) 6
b) 8
c) 4
d) 9

Answer : D

Question. Which of the following represents coinitial vector?
a) Both (a) and (b)
b) m, b
c) c, d
d) b, d

Answer : A

Question. Find the ratio in which 2x + 3y + 5z = 1 divides the line joining the points (1, 0, -3) and (1. -5. 7) is
a) a
b) b
c) d
d) c

Answer : A

Question. If a + b + c = 0, then a × b =
a) c × a
b) 0
c) b × c
d) Both (a) and (b)

Answer : D

Question. The position vector of the point (1, 2, 0) is:
a) 2j + k
b) i + j +k
c) i + 2j
d) i + 2j + k

Answer : C

Question. Three points (2, -1, 3), (3, – 5, 1) and (-1, 11, 9) are
a) None of these
b) Collinear
c) Non-collinear
d) Non-coplanar

Answer : B

Question. Can two different vectors have the same magnitude?
a) Cannot be determined
b) Yes
c) None of the above
d) No

Answer : B

Question. A point from a vector starts is called ____ and where it ends is called its ____.
a) initial point, terminal point
b) initial point, endpoint
c) terminal point, endpoint.
d) origin, endpoint

Answer : A

Question. If a, b, c are unit vectors such that a + b + c = 0, then the value of a.b + b.c + c.a is
(a) 1 
(b) 3
(c) - (3/2)
(d) None of these
a) a
b) b
c) c
d) d

Answer : C

Question. Time period is a ________
a) Vector quantity
b) Neither scalar nor vector
c) Scalar quantity
d) None of these

Answer : C

Question. The points with position vectors (2. 6), (1, 2) and (a, 10) are collinear if the of a is
a) 4
b) -8
c) 3
d) 12

Answer : C

Question. Let a, b and c be vectors with magnitudes 3, 4 and 5 respectively and a + b + c = 0, then the values of a . b + b . c + c . a is
a) 47
b) 50
c) -25
d) 25

Answer : C

Question. If (1/2, 1/3, n) are the direction cosines of a line, then the value of n is
(a) √23/6
(b) 23/6
(c) 2/3
(d) 3/2
a) b
b) d
c) c
d) a

Answer : D

Question. The length of longer diagronal of the parallelogram constructed on 5a + 2b and a -3b. If it is given that │a│= 2√2, │b│ = 3 and angle between a and b is π/4, is
(a) 15
(b) √113
(c) √593
(d) √369
a) a
b) d
c) c
d) b

Answer : C

Question. Which of the following represents collinear but not equal vectors?
a) a, c
b) b, d
c) b, m
d) Both (a) and (b)

Answer : A