The number of distinct real values of `alpha`, for which the vectors `-lamda^(2) hati +hatj+hatk, hati -lamda^(2)hatj +hatk and hati +hatj -lamda^(2)hatk` are coplanar is

Options

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

Answer

C

Explanation

Since given vectors are coplanar
`:. |{:(-lambda^(2),,1,,1),(1,,-lambda^(2),,1),(1,,1,,-lambda^(2)):}|=0`
`rArr lambda^(6) - 3lambda^(2) - 2= 0 rArr (1+lambda^(2))^(2) (lambda^(2)-2) =0 rArr lambda =+- sqrt(2)`