The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2 \hat{i}+\hat{j}+\

Question

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

Professor PC Thomas Classes · Answer

Determinant of components = 0. Solving $-\lambda^2(\lambda^4-1) - 1(-\lambda^2-1) + 1(1+\lambda^2) = 0 \implies \lambda^2=1$. Real $\lambda = \pm 1$.