The number of distinct values of λ, for which the vectors $-λ^2\hat i+\hat j+\hat k, \hat i-λ^2\hat j+\hat k$ and $\hat i+\hat j-λ^2\hat k$ are coplanar, is

2

Given vectors will be coplanar, if

$\begin{vmatrix}-λ^2 &1& 1\\ 1& -λ^2& 1\\1&1&-λ^2\end{vmatrix} =0$

$⇒ λ^6-3λ^2-2=0⇒ (1+λ^2)^2 (λ^2-2)=0⇒ λ=±\sqrt{2}$

There are 2 values of $\lambda$.