NDA MATHS QUESTION BANK

54. What is the vector in the xy-plane
    through origin and perpendicular to
    the vector r= ai + bj and of the same
    length?
    (a) –ai – bj (b) ai – bj (c) – ai + bj (d) bi

• aj

55. 
    

    The magnitude of the vectors a and
    b are equal and the angle between
    them is 60. If the vectors λa + b and a –
    λb are perpendicular of each other,
    what is the value of λ?
    (a) 1 (b) 2 (c) 3 (d) 4

    
    


56. 
    

    Consider the diagonals of a
    quadrilateral formed by the vectors 3i

    
    

• 6j – 2k and 4i – j + 3k. The
  quadrilateral must be a
  (a) square (b) rhombus (c) rectangle
  (d) None of these

57. 
    

    If | | | | and | | ,
    what is the value of a. b?
    (a) 4 (b) 6 (c) 8 (d) 10

    
    


58. 
    

    If a = I – 2j + 5k and b = 2i + j – 3k,
    what is (b – a). (3a + b) equal to?
    (a) 106 (b) -106 (c) 53 (d) – 53

    
    


59. 
    

    If (3a – b)×(a + 3b)= ka × b, what is
    the value of k?
    (a) 10 (b) 5 (c) 8 (d) - 8

    
    


60. 
    

    If a and b are unit vectors, what is
    the value of | |^ ( )^?

    
    

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

61. If a and b are two unit vectors
    inclined at an angle 60 to each other,
    which one of the following is correct?

(a) | | (b) | | (c)

| | (d) | |

62. If a= 2i – 3j – k and b= i + 4j – 2k,

what (a + b) × (a – b) equal to?

(a) 2 (a × b) (b) -2 (a × b) (c) (a × b)

(d) – (a × b)

63. If a, b and c are unit vectors such

that a is perpendicular to the plane of b,

c and the angle between b and c is^.

What is the value of | |?

(a) 1 (b) 2 (c) 3 (d) 4

64. What is the locus of the point (x, y)

for which the vectors (i – xj – 2k) and

(2i + j + yk) are orthogonal?

(a) A circle (b) An ellipse (c) A

parabola (d) A straight line

65. If ai + j + k, i + bj + k and i + j + ck are

coplanar vectors, what is the value of a

+ b + c – abc?

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

66. If a= i + 2j – 3k and b= 3i – j + λk

and (a + b) is perpendicular to a – b,

what is the value of λ?

(a) -2 (b) ± 2 (c) 3 (d) ± 3

67. Two vectors 2i + mj – 3nk and 5i +

3mj + nk are such that their magnitudes

are respectively √ and √ , where m

and n are integers. Which one of the

following is correct?

(a) m takes 1 value and n takes 1 value

(b) m takes 1 value and n takes 2

values

(c) m takes 2 values and n takes 1 value

(d) m takes 2 values and n takes 2

values