Let `veca=hati+hatj+hatk, vecb=hati-hatj+2hatk and vecc=xhati+(x-2)hatj-hatk`. If the vector `vecc` lies in the plane of `veca and vecb` then x equals (A) 0 (B) 1 (C) -4 (D) -2

Options

A. 0
B. 1
C. `-4`
D. `-2`

Answer

D

Explanation

Since, given vectors a, b and c are coplanar.
`:. |{:(1,1,1),(1,-1,2),(x,x-2,-1):}| = 0`
`rArr 1{1-2(x-2)} -1(-1-2x)+ 1(x-2 +x) = 0`
`rArr 1 -2x + 4 + 1 + 2x + 2x- 2 = 0`
`rArr 2x = - 4`
`x = - 2`