Question

A unit vector normal to the plane through the points $\hat{i},2\hat{j}$ and $3\hat{k}$ is

• A. $\frac{-6\hat{i}+3\hat{j}+2\hat{k}}{7}$
• B. $\frac{6\hat{i}+3\hat{j}-2\hat{k}}{7}$
• C. $\frac{6\hat{i}+3\hat{j}+2\hat{k}}{7}$
• D. $\frac{6\hat{i}-3\hat{j}+2\hat{k}}{7}$

Answer 1

The correct option is C $\frac{6\hat{i}+3\hat{j}+2\hat{k}}{7}$

Let $\overrightarrow{a}=\hat{i},\overrightarrow{b}=2\hat{j},\overrightarrow{c}=3\hat{k}$
Direction of normal vector$=(\overrightarrow{b}-\overrightarrow{a})\times (\overrightarrow{c}-\overrightarrow{b})$
$=(2\hat{j}-\hat{i})\times (3\hat{k}-2\hat{j})$
$=6\hat{i}+3\hat{j}+2\hat{k}$

$\therefore$ unit vector along normal
$=\pm \frac{6\hat{i}+3\hat{j}+2\hat{k}}{7}$