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. zero
B. one
C. two
D. three

Answer

C

Explanation

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