Question

If the vectors `2hati-qhatj+3hatk and 4hati-5hatj+6hatk` are collinear, then value of q is

(A) 5

(B) 10

(C) 5/2

(D) 5/4

Answer 1

(C) 5/2

Let `bar a=2hati-qhatj+3hatk and barb=4hati-5hatj+6hatk`

Since, `bara and barb` are collinear.
∴ there exists a scalar t such that `barb = t bara `.

∴  `4hati-5hatj+6hatk=t(2hati-qhatj+3hatk)=2thati-qthatj+3thatk`

∴ By equality of vectors, we get

  4 = 2t, - 5 = - qt, 6 = 3t

∵ 4 = 2t and 6 = 3t  ∴t = 2

- 5 =- q(2)
–5 = – 2q 

∴ 5 = 2q
q = 5/2