Question

The unit vector normal to the plane $x+2y+3z-6=0$ is $\frac{1}{\sqrt{14}}\hat{i}+\frac{2}{\sqrt{14}}\hat{j}+\frac{3}{\sqrt{14}}\hat{i}$
State true or false

• A. True
• B. False

Answer 1

The correct option is A True

Given plane : $x+2y+3z-6=0$
Normal vector to the plane
$\overrightarrow{n}=\hat{i}+2\hat{j}+3\hat{k}$
Magnitude of the normal vector :
$|\overrightarrow{n}|=\sqrt{1^2+2^2+3^2}$
Unit normal vector to the plane :
$\Rightarrow \frac{(\hat{i}+2\hat{j}+3\hat{k})}{\sqrt{14}}=\frac{1}{\sqrt{14}}\hat{i}+\frac{2}{\sqrt{14}}\hat{j}+\frac{3}{\sqrt{14}}\hat{k}$
Hence , the given statement is true .