Question

If vectors $\hat{i}+\hat{j}+\hat{k},\hat{i}-\hat{j}+\hat{k}$ and $2\hat{i}+3\hat{j}+\lambda \hat{k}$ are coplanar, then $\lambda$ is equal to

• A. $-2$
• B. $3$
• C. $2$
• D. $-3$

Answer 1

The correct option is C $2$

Since, vectors $\hat{i}+\hat{j}+\hat{k},\hat{i}-\hat{j}+\hat{k}$ and $2\hat{i}+3\hat{j}+\lambda \hat{k}$ are coplanar, then
$\left|\begin{array}{ccc}1& 1& 1\\ 1& -1& 1\\ 2& 3& \lambda \end{array}\right|=0$
$\Rightarrow 1(-\lambda -3)-1(\lambda -2)+1(3+2)=0$
$\Rightarrow -\lambda -3-\lambda +2+5=0$
$\Rightarrow 2\lambda =4$
$\Rightarrow \lambda =2$