Question

The value of x such that the vectors $a=2\hat{i}-\hat{j}+\hat{k},b=x\hat{i}+2\hat{j}-3\hat{k}$ and $c=3\hat{i}-4\hat{j}+5\hat{k}$ are coplanar is

• A. 1
• B. 3
• C. -2
• D. 0

Answer 1

The correct option is A 1

$a=2\hat{i}-\hat{j}+\hat{k},b=x\hat{i}+2\hat{j}-3\hat{k}$ and $c=3\hat{i}-4\hat{j}+5\hat{k}$ are coplanar

$\Rightarrow \left|\begin{array}{ccc}2& -1& 1\\ x& 2& -3\\ 3& -4& 5\end{array}\right|=0$

$\Rightarrow -4+5x+9-4x-6=0$

$\therefore x=1$

Hence, option A.