The number of distinct values of `lamda`, 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

Given vectors will be coplanar if
`|(-lamda^(2),1,1),(1,-lamda^(2),1),(1,1,-lamda^(2))|=0`
`implieslamda^(6)-3lamda^(2)-2=0implies(1+lamda^(2))^(2)(lamda^(2)-2)=0implieslamda=+-sqrt(2)`