Question

The unit normal to the plane 2x + y + 2z = 6 can be expressed in the vector form as

पर्याय

• ${\displaystyle i3+j2+k2}$

• ${\displaystyle i\frac{2}{3}+j\frac{1}{3}+k\frac{2}{3}}$

• ${\displaystyle i\frac{1}{3}+j\frac{1}{2}+k\frac{1}{2}}$

• ${\displaystyle i\frac{1}{3}+j\frac{1}{3}+k\frac{2}{3}}$

Answer 1

${\displaystyle i\frac{2}{3}+j\frac{1}{3}+k\frac{2}{3}}$

Explanation:

Equation of the plane, ${\displaystyle 2x+y+2z}$ = 6

∴ Normal vector, ${\displaystyle \overrightarrow{n}=(2,1,2)}$

${\displaystyle \left|\overrightarrow{n}\right|=\sqrt{2^2+1^2+2^2}}$ = 3

⇒ Unit normal vector, ${\displaystyle \hat{n}=\frac{\overrightarrow{n}}{\left|\overrightarrow{n}\right|}=\frac{\left(2\text{,}1\text{,}2\right)}{3}}$

∴ ${\displaystyle \hat{n}=\frac{2}{3}\hat{i}+\frac{\hat{j}}{3}+\frac{2}{3}\hat{k}}$