jee-advanced 2007 Q55

jee-advanced · India · paper1 Vector Product and Surfaces
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
(A) 0
(B) 1
(C) 2
(D) 3
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\\
(A) 0\\
(B) 1\\
(C) 2\\
(D) 3