Question

If two vectors $2\hat{i}+3\hat{j}-\hat{k}$ and $-4\hat{i}-6\hat{j}+\lambda \hat{k}$ are parallel to each other, then value of $\lambda$ will be

• A. $0$
• B. $3$
• C. $2$
• D. $4$

Answer 1

The correct option is C $2$

Given, two vectors are,
$\overrightarrow{A}=2\hat{i}+3\hat{j}-\hat{k}$
$\overrightarrow{B}=-4\hat{i}-6\hat{j}+\lambda \hat{k}$

When two vectors are parallel to each other, then
$\frac{a_x}{b_x}$=$\frac{a_y}{b_y}=\frac{a_z}{b_z}$

$\frac{2}{-4}$=$\frac{3}{-6}=\frac{-1}{\lambda }$

$\frac{1}{2}=\frac{1}{\lambda }$

$\Rightarrow \lambda =2$

Final answer: (b).