The number of real values of a for which the vectors `hati+2hatj+hatk, ahati+hatj+2hatk` and `hati+2hatj+ahatk` are coplanar is

Options

A. 1
B. 2
C. 3
D. 0

Answer

A

Explanation

For given vectors to be coplanar, we must have
`|(1,2,1),(a,1,2),(1,2,a)|=0`
`=(a-4)-2(a^(2)-2)+(2a-1)=0`
`implies2a^(2)-3a+=0implies(2a-1)(a-1)=0impliesa=1, 1/2` Hence there are two values of `a`