Question

The two vectors $\{\overrightarrow{a}=2\hat{i}+\hat{j}+3\hat{k},\overrightarrow{b}=4\hat{i}-\lambda \hat{j}+6\hat{k}\}$ are parallel if $\lambda$ is equal to

• A. $2$
• B. $-3$
• C. $3$
• D. $-2$

Answer 1

The correct option is D $-2$

For parallel $\overrightarrow{a}\times \overrightarrow{b}=0$
$\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 1& 3\\ 4& -\lambda & 6\end{array}\right|=0$
$\Rightarrow \hat{i}(6+3\lambda )-\hat{j}\left(0\right)+\hat{k}(-2\lambda -4)=0$
$=0.\hat{i}+0.\hat{j}+0.\hat{k}$
$\therefore 6+3\lambda =0\Rightarrow \lambda =-2$