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.
$⇒ \left(\begin{vmatrix} 2 &-3 &4 \\ 2& 1 &-1 \\ \lambda & -1 &2 \end{vmatrix} = 0\right)$
$\Rightarrow 2(1)+3(4+\lambda)+4(-2-\lambda)=0$
$\Rightarrow 2+12+3 \lambda-8-4 \lambda=0$
$\Rightarrow \lambda=6$