CBSE Class 12 Mathematics Vectors Algebra MCQs Set 05

Question. If the vectors 2i+j+ k and i-4j+λ k are perpendicular, then λ is equal to
(a) 4
(b) -5
(c) 2
(d) 1

Answer: C

Question. If a and b are two unit vectors such that a b + 2 and 5a- 4b - are perpendicular to each other, then the angle between a and b is
(a) 30°
(b) 60°
(c) cos- 1(3/5)
(d) cos- 1(4/7)

Answer: B

Question. If θ is the angle between the vectors a and band| axb|= |a,b| then θ is
(a) 0
(b) 180°
(c) 135°
(d) 45°

Answer: D

Question. For non-zero vector a and b, if |a+b|< |a-b|, then a and b are
(a) collinear
(b) perpendicular to each other
(c) inclined at an acute angle
(d) inclined at an obtuse angle

Answer: D

Question. If a and b are unit vectors, then the greatest value of
|a+b |+ |a-b| is
(a) 2
(b) 4
(c) 2√2
(d) √2

Answer: C

Question. If a, b and c are non-coplanar vectors and r is a real number, then the vectors a+2b +3c, λb+4c and
(2λ- 1)c are non-coplanar for
(a) no value ofλ
(b) all except one value of λ
(c) all except two values of λ
(d) all values ofλ

Answer: C

Question. If for a unit vector a, (x -a)· (x+a) = 12, then|x| is equal to
(a) 4
(b) 2
(c) 13
(d) 11

Answer: C

Question. Let u v, and w be three vectors such that |u | =1|v |=2,|w| = 3. If the projection of v along u is equal to that of w along u , v and w are perpendicular to each other, then |u-v+w| is equal to
(a) 4
(b) √7
(c) √14
(d) 2

Answer: C

Question. Let ABCD be a parallelogram whose diagonals intersect at P and let O be the origin, then OA+ OB+ OC+ OD equal to
(a) OP
(b) 2OP
(c) 3OP
(d) 4OP

Answer: D

Question. If ABCD is a rhombus whose diagonals cut at the origin O, then OA+ OB+ OC+ OD equals
(a) AB+ AC 
(b) O
(c) 2(AB +BC)
(d) AC+ BD 

Answer: B

Question. A point O is the centre of circle circumscribed about a ΔABC. Then,OA sin2A+0B sin2B+0C sin 2C is equal to
(a) ( OA+OB+OC))sin 2A
(b) 3OG, where Gis centroid of ΔABC
(c) O
(d) None of the above 

Answer: C

Question. If DA a AB b = = , and CB a =k , wherek > 0and X Y, are the mid-points of DB and AC respectively such that |a| =17 and | XY | =4, then k is
equal to
(a) 8/17
(b) 9/17
(c) 5/17
(d) 4/17

Answer: B

Question. If a and b are two unit vectors inclined to x-axis at angles 30° and 120°, then| | a b + is equal to

(a)√2/3
(b)√2
(c)√3
(d)2

Answer: B

Question. The sum of two unit vectors is a unit vector. The magnitude of their difference is
(a) 2
(b) √3
(c) √2
(d) 1

Answer: B

Question. If a and bare position vectors of A and B respectively and C is a point on AB produced such that AC= 3AB then position vector of C is
(a) 3a -2b 
(b) 3b- 2a
(c) 3b+ 2a
(d) 2a-3b

Answer: B

Question. ABCD is a parallelogram, A₁ and B₁are mid-points of side BC and CD respectively. If AA₁+ BB₁ = λAC then λ is equal to
(a) 1/2
(b) 1
(c) 3/2
(d) 2

Answer: C

Question. The angle between and b is π/6, then angle between 2a and 3b is
(a) π/3
(b) π/2
(c) π/6
(d) 3π/4

Answer: C

Question. If|a |b |c| and a+ b= c, then the angle between a and b is
(a) π /2
(b) p
(c) 0
(d) None of these 

Answer: C

Question. Find the position vector of point R which divides the line joining two points p(2a+b) and Q(a-3b) externally in the ratio 1:2 . Also, show that P is the middle point of the line segment RQ. 
(a) 2a + b
(b) 5a+ 3b 
(c) 3a+ 5b
(d) None of these

Answer: C

Question. The angle between two vectors a and b with magnitudes √3 and 2 respectively, having a ·b = √6 is 
(a) √/4
(b) π/2
(c) π/6
(d) π/3

Answer: A

Question. Vectors a and b are such that |a|=1,| b|=4 and a · b× = 2. If c =2axb- 3b , then the angle between b and c is
(a) π/6
(b) 5/π
(c) π/3
(d) 2π/3

Answer: B

Question. For any two non-zero vectors a and b, |a |b+| b| a and |a| b-| b| a are 
(a) parallel
(b) perpendicular
(c) non-parallel
(d) None of these

Answer: B

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) 0
(b) -1/2
(c) -3/2
(d) 2/11.

Answer: C

Question. If the vertices A, B, C of a ΔABC have position vectors (1,2,3), (-1,0,0),(0,1,2) respectively, then ∠ABC (∠ABC is the angle between the vectors BA and BC), is equal to 
(a)π/2
(b) π/4
(c) cos^-1(10/√102)
(d) cos^-1(1/3)

Answer: C

Question. If a· a× = 0 and a· b = 0, then what can be conclude about the vector b? 
(a) Any vector
(b) Zero-vector
(c) Unit vector
(d) None of these 

Answer: A

Question. Given that a· b = 0 and ax b = 0. What can you conclude about the vectors a and b? 
(a) a and b can be perpendicular and parallel simultaneously
(b) |a| = 0 or |b| = 0
(c) |a| = 0 and |b| = 0
(d) None of the above

Answer: B

Question. The points A(1,2,7), B( 2,6,3) and C( 3,10,-1) are
(a) collinear
(b) coplanar
(c) non-collinear
(d) None of these 

Answer: A

Question. If a = b+ c, then which of the following statements is correct? 
(a) | a| =|= |c| 
(b) | a|+|b| =|c| 
(c) | a|b| +|c|
(d) None of these

Answer: C

Question. (ax b)x= ax(b x c) if
(a) (a x b)x c =0 
(b) c x a=b 
(c) (a x c) x b =0
(d) a·(b x c)

Answer: C