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. `-2`
D. 2

Answer

C

Explanation

Given, `a=hati+hatj+hatk, b=hati-hatj+2hatk`
and `c=xhati+(x-2)hatj-hatk`
Since, c lies in the plane of vectors a and b, therefore a, b and c are coplanar.
`therefore |(1,1,1),(1,-1,2),(x,(x-2),-1)|=0`
`implies 1(1-2x+4)-1(-1-2x)+1(x-2+x)=0`
`implies 5-2x+1+2x+2x-2=0`
`implies x = - 2 `