Question

What is the value of m if the vectors $2\hat{i}-\hat{j}+\hat{k},\hat{i}+2\hat{j}-3\hat{k}$ and $3\hat{i}+m\hat{j}+5\hat{k}$ are coplanar?

• A. -2
• B. 2
• C. -4
• D. 4

Answer 1

The correct option is C -4

For any three vectors to be coplanar, scalar triple product should be zero.

So, we have

$\left|\begin{array}{ccc}2& -1& 1\\ 1& 2& -3\\ 3& m& 5\end{array}\right|=0\Rightarrow 2\times \left(\right(2\times 5)-(-3\times m\left)\right)-(-1)\left(\right(1\times 5)-(-3\times 3\left)\right)+1\times \left(\right(1\times m)-(2\times 3\left)\right)=0\Rightarrow 20+6m+5+9+m-6=0\Rightarrow m=\frac{6-9-20-5}{7}=-4$

So value of m is -4.