CBSE Class 12 Mathematics Vectors Algebra MCQs Set 03

Question. ABC is a triangle and P is any point on BC such that P̅Q̅ is the resultant of the vectors A̅P̅ , P̅B̅ and P̅C̅ , then
(a) the position of Q depends on position of P
(b) Q is a fixed point
(c) Q lies on AB or AC
(d) None of these

Answer : B

Question. If the positive numbers a, b and c are the pth, qth and rth terms of GP, then the vectors log1

(a) equal
(b) parallel
(c) perpendicular
(d) None of these

Answer : C

Question. If|a|=|b||c|=1 and a·b = b ·c = cos θ, then the maximum value of θ is
(a) π/3
(b) π/2
(c) 2√/3
(d) 2π/5

Answer : C

Question. If a, b and c are coplanar vectors and λ is a real number, then the vectors a+ 2b+ 3c, λb +µc l and (2λ -1)c are coplanar for
(a) all values ofµ
(b) λ = 1/2
(c) λ = 0
(d) all of the options

Answer : D

Question. If a is a unit vector and projection of x along a is 2 and ax r+ b= r, is equal to

Answer : B

Question. Let a ,b and c be three unit vectors such that a is perpendicular to the plane of b and c. If the angle between

(a) 1/3
(b) 1/2
(c)1
(d) 2

Answer : C

Question.

Answer : A

Question. If a + 2b + 3c = 0, then a x b + b x c + c x a = ra x b 
Where R is equal to
(a) 0
(b) 1
(c) 2
(d) 3

Answer : C

Question.

Answer : D

Question. If A(-4,0, 3) and B(14,2,-5), then which one of the following points lie on the bisector of the angle between OA and OB(O is the origin of reference)?
(a) (2 ,2 ,4)
(b) (2,11,5)
(c) (-3,- 3,- 6)
(d) (1 1,2)

Answer : A, B, D

Question.

Answer : B

Question.

Answer : A, B, D

Question. a and b are two given vectors. With these vectors as adjacent sides, a parallelogram is constructed. The vector which is the altitude of the parallelogram and which is perpendicular to a is

Answer : A, B, C

Question. If three points A, B and C have position vectors (1, x, 3), (3, 4, 7) and (y, – 2, – 5) respectively and, if they are collinear, then (x – y) is equal to
(a) (2, – 3)
(b) (– 2, 3)
(c) (2, 3)
(d) (– 2, – 3)

Answer : A

Question.

(a) 3
(b) 0
(c) 1
(d) 2

Answer : A

Question. If a̅ = î + 2ĵ + 3k̂ , b̅ = 2î + 3ĵ + k̂ , c̅ = 3î + ĵ + 2k̂ and α a̅ + βb̅ + ϒc̅ = -3(î – k̂) , then the ordered triplet (α, β, ϒ) is
(a) (2, –1, –1)
(b) (–2, 1, 1)
(c) (–2, –1, 1)
(d) (2, 1, –1)

Answer : A

Question. A unit vector perpendicular to the plane formed by the points (1, 0, 1), (0, 2, 2) and (3, 3, 0) is
(a) 1/5√3 (5î – ĵ -7k̂)
(b) 1/5√3 (5î – ĵ + 7k̂)
(c) 1/5√3 (5î -+ ĵ + 7k̂)
(d) None of these

Answer : B

Question. A girls walks 4 km towards West. Then, she walks 3 km in a direction 30° East to North and stops. The girls displacement from her initial point of departure is

Answer : C

Question. ABCD is a parallelogram whose diagonals meet at P. If O is a fixed point, then O̅A̅ + O̅B̅ + O̅C̅ + O̅D̅ equals
(a) O̅P̅
(b) 2 O̅P̅
(c) 3 O̅P̅
(d) 4 O̅P̅

Answer : D

Question. If the vertices of any tetrahedron be A̅ = J̅ + 2K̅ , B̅ = 3I̅ + K̅ ,

(a) 1/6 units
(b) 6 units
(c) 36 units
(d) None of these

Answer : B

Question. A vector whose magnitude is the same as that of a given vector, but direction is opposite to that of it, is called
(a) negative of the given vector
(b) equal vector
(c) null vector
(d) collinear vector

Answer : A

Question. a̅ , b̅ , c̅ are 3 vectors, such that a̅ + b̅ + c̅ = 0 , |a̅| = 1 , |b̅| = 2 , |c̅| = 3 , , then a̅.b̅ + b̅.c̅ + c̅.a̅ is equal to
(a) 1
(b) 0
(c) – 7
(d) 7

Answer : C

Question. Two or more vectors having the same initial point are called
(a) unit vectors
(b) zero vectors
(c) coinitial vectors
(d) collinear vectors

Answer : C

Question. The non-zero vectors are a̅ , b̅ and c̅ are related by a̅ = 8b̅ and c̅ = -7b̅ . Then the angle between a̅ and c̅ is
(a) 0
(b) π/4
(c) π/2
(d) π

Answer : D

Question. The vectors

(a) x = 1, y = – 2, z = – 5
(b) x = 1/2, y = – 4, z = – 10
(c) x = – 1/2, y = 4, z = 10
(d) All of these

Answer : D

Question. If b̅ and c̅ are any two non-collinear mutually perpendicular unit vectors and a̅ is any vector, then

(a) a̅
(b) 2a̅
(c) 3a̅
(d) None

Answer : A

Question. The angle between the vectors a̅ + b̅ and a̅ – b̅ , where a̅ = (1, 1, 4) and b̅ = (1, –1, 4) is
(a) 90°
(b) 45°
(c) 30°
(d) 15°

Answer : A

Question. If (a̅ x b̅)2 + (a̅.b̅)2 = 676 and |b̅| = 2 , then |a̅| is equal to
(a) 13
(b) 26
(c) 39
(d) None of these

Answer : A

Question. If | a̅ + b̅ |= a̅ – b̅ | then the vectors a̅ and b̅ are adjacent sides of
(a) a rectangle
(b) a square
(c) a rhombus
(d) None of these

Answer : A

Question. For any vector a̅ , the value of

(a) a̅2
(b) 3a̅2
(c) 4a̅2
(d) 2a̅2

Answer : D

Question. If a girl moves from A to B and then from B to C (as shown). Then, net displacement made by the girl from A to C, is

(a) AB – BC = AC
(b) AC = AB – BC
(c) AC = AB + BC
(d) None of these

Answer : C

Question.

Answer : A

Question. A zero vector has
(a) any direction
(b) no direction
(c) many directions
(d) None of these

Answer : B