A plane makes 2,1,-2 intercepts on co-ordinate axes. Its distance… - Vidyadip

MCQ

A plane makes $2,1,-2$ intercepts on co-ordinate axes. Its distance from the origin is

A
3
B
$\frac{1}{3}$
✓
$\frac{2}{\sqrt{6}}$
D
$\sqrt{6}$

✓

Answer

Correct option: C.

$\frac{2}{\sqrt{6}}$

(C)
Let the intercepts made by the plane $a , b , c =2,1,-2$
$\therefore \quad$ The distance of plane from origin is
$d=\frac{1}{\sqrt{\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}}}$
$=\frac{1}{\sqrt{\frac{1}{4}+1+\frac{1}{4}}}=\frac{2}{\sqrt{6}}$
Alternate method:
The equation of plane is
$\frac{x}{2}+\frac{y}{1}+\frac{z}{-2}=1$
i.e. $x+2 y-z-2=0$
∴ distance of plane from the origin is
$d=\left|\frac{-2}{\sqrt{1+4+1}}\right|$
$d =\frac{2}{\sqrt{6}}$

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