Question

The length of perpendicular from the origin to the plane which makes intercepts $\frac{1}{3},\frac{1}{4},\frac{1}{5}$ respectively on the coordinate axes is

• A. $\frac{1}{5\sqrt{2}}$
• B. $\frac{1}{10}$
• C. $5\sqrt{2}$
• D. $5$

Answer 1

Answer: (A)

$\frac{1}{5\sqrt{2}}$

Equation of plane in intercept form is, $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$

$\Rightarrow 3x+4y+5y-1=0$, Substitute given intercepts

Hence distance from origin $=\left|\frac{0+0+0-1}{\sqrt{3^2+4^2+5^2}}\right|=\frac{1}{\sqrt{50}}=\frac{1}{5\sqrt{2}}$