Exercise 8.5: Choose the correct answer

Vector Algebra (Mathematics)

Choose the correct or the most suitable answer from the given four alternatives

(1) The value of   is 

Ans: (3)

Solution

(2) If  are parallel, then the value of m is 

 (1) 3 

(2) 1/3 

(3) 6 

(4) 1/6

Ans: (3)

Solution

(3) The unit vector parallel to the resultant of the vectors iˆ + jˆ − kˆ and iˆ − 2 jˆ + kˆ is 

(1) iˆ − jˆ + kˆ  /√5

(2) 2iˆ + jˆ  /√5

(3) 2iˆ − jˆ + kˆ /√5 

(4) 2iˆ − jˆ /√5

Ans: (4)

Solution

(4) A vector  makes 60° and 45° with the positive direction of the x and y axes respectively. Then the angle between  and the z-axis is 

(1) 45° 

(2) 60° 

(3) 90° 

(4) 30°

Ans: (2)

Solution

(5) If = 3iˆ + 2 jˆ + kˆ and the position vector of B is iˆ + 3jˆ − kˆ, then the position vector A is

(1) 4iˆ + 2 jˆ + kˆ 

(2) 4iˆ + 5 jˆ 

(3) 4iˆ 

(4) −4iˆ

Ans: (2)

Solution

(6)  A vector makes equal angle with the positive direction of the coordinate axes. Then each angle is equal to

(1) cos^-1 (−1/3) 

(2) cos⁻¹ (2/3) 

(3) cos⁻¹ (1/√3) 

(4) cos⁻¹ (2/√3)

Ans: (3)

Solution

7) The vectors  are

(1) parallel to each other

(2) unit vectors 

(3) mutually perpendicular vectors

(4) coplanar vectors

Ans: (4)

(8) If ABCD is a parallelogram, then  is equal to

Ans: (4)

Solution

(9) One of the diagonals of parallelogram ABCD with   and  as adjacent sides is  + . The other diagonal  is 

Ans: (2)

Solution

(10) If  ,  are the position vectors A and B, then which one of the following points whose position vector lies on AB, is 

Ans: (3)

Solution

(11) If  , ,  are the position vectors of three collinear points, then which of the following is true? 

Ans: (2)

Solution

(12) If  , then the point P whose position vector  divides the line joining the points with position vectors  and  in the ratio 

(1) 7 : 9 internally 

(2) 9 : 7 internally 

(3) 9 : 7 externally 

(4) 7 : 9 externally 

Ans: (1)

Solution

(13) If λiˆ + 2λjˆ + 2λkˆ is a unit vector, then the value of λ is 

(1) 1/3 

(2) 1/4 

(3) 1/9 

(4) 1/2

Ans: (1)

Solution

(14) Two vertices of a triangle have position vectors 3iˆ + 4 ˆj − 4kˆ and 2iˆ + 3 ˆj + 4kˆ. If the position vector of the centroid is iˆ + 2 ˆj + 3kˆ, then the position vector of the third vertex is

(1) −2iˆ − jˆ + 9kˆ 

(2) −2iˆ − jˆ − 6kˆ 

(3) 2iˆ − jˆ + 6kˆ 

(4) −2iˆ + jˆ + 6kˆ

Ans: (1)

Solution

(15) If |  +  | = 60,| - | = 40 and |  | = 46, then  is 

 (1) 42 

(2) 12 

(3) 22 

(4) 32 

Ans: (3)

Solution

(16) If   and , having same magnitude and angle between them is 60º and their scalar product is 1/2 then |  | is 

(1) 2 

(2) 3 

(3) 7 

(4) 1 

Ans: (4)

Solution

(17) The value of θ ∈ (0, π/2) for which the vectors  are perpendicular, is equal to 

(1) π /3

(2) π/6 

(3) π/4 

(4) π/2 

Ans: (1)

Solution

(18)  If |  |= 13, |  |= 5 and  ⋅  = 60° then |  ×  | is 

(1) 15 

(2) 35 

(3) 45 

(4) 25 

Ans: (4)

Solution

(19) Vectors  and  are inclined at an angle θ = 120º. If |  |= 1,|  |= 2 , then [(+ 3 ) × (3 − )]²  is equal to 

 (1) 225 

(2) 275 

(3) 325 

(4) 300 

Ans: (4)

Solution

(20) If  and  are two vectors of magnitude 2 and inclined at an angle 60º , then the angle between  and  +  is 

(1) 30° 

(2) 60° 

(3) 45° 

(4) 90° 

Ans: (1)

Solution

(21) If the projection of   5iˆ − jˆ − 3kˆ on the vector iˆ + 3jˆ + λkˆ is same as the projection of iˆ + 3 jˆ + λkˆ on 5iˆ − jˆ − 3kˆ, then λ is equal to

 (1) ± 4 

(2) ± 3 

(3) ± 5 

(4) ±1 

Ans: (3)

Solution

(22) If (1, 2, 4) and (2, - 3λ - 3) are the initial and terminal points of the vector iˆ + 5 ˆj − 7kˆ , then the value of λ is equal to

(1) 7/3 

(2) − 7/3 

(3) − 5/3 

(4) 5

Ans: (2)

Solution

(23) If the points whose position vectors 10iˆ + 3 ˆj , 12iˆ − 5 ˆj and aiˆ +11ˆj are collinear then a is equal to

 (1) 6 

(2) 3 

(3) 5 

(4) 8 

Ans: (4)

Solution

(24)  If  = iˆ + jˆ + kˆ,  = 2iˆ + xjˆ + kˆ,  = iˆ − jˆ + 4kˆ and  ⋅ ( × ) = 70 , then x is equal to

 (1) 5 

(2) 7 

(3) 26 

(4) 10 

Ans: (3)

Solution

(25) If  = iˆ + 2 jˆ + 2kˆ, |  |= 5 and the angle between  and  is π/6 , then the area of the triangle formed by these two vectors as two sides, is 

 (1) 7/4 

(2) 15/4 

(3) 3/4 

(4) 17/4 

Ans: (2)

Solution