Question

If the vectors $2\hat{i}-3\hat{j}+4\hat{k},2\hat{i}+\hat{j}-\hat{k}$ and $\lambda \hat{i}-\hat{j}+2\hat{k}$ are coplanar, then the value of $\lambda$ is

• A. 6
• B. -5
• C. -6
• D. 5

Answer 1

Answer: (A)

Given vectors are coplanar.
$\Rightarrow \left(\left|\begin{array}{ccc}2& -3& 4\\ 2& 1& -1\\ \lambda & -1& 2\end{array}\right|=0\right)$
$\Rightarrow 2(1)+3(4+\lambda )+4(-2-\lambda )=0$
$\Rightarrow 2+12+3\lambda -8-4\lambda =0$
$\Rightarrow \lambda =6$