Question

If for a plane, the intercepts on the co-ordinate axes are $8,4,4$ ; then the length of the perpendicular from the origin on to the plane is ?

• A. $\frac{8}{3}$
• B. $\frac{3}{8}$
• C. $3$
• D. $\frac{4}{3}$

Answer 1

Answer: (A)

$\frac{8}{3}$

Given for a plane intercepts on co-ordinate axis are 8,4,4.

so, the equation of plane is $\frac{x}{8}+\frac{y}{4}+\frac{z}{4}=1$

The length of perpendicular from origin to the plane is $\left|\frac{0+0+0+1}{\sqrt{{\left(\frac{1}{8}\right)}^2+{\left(\frac{1}{4}\right)}^2+{\left(\frac{1}{4}\right)}^2}}\right|$

= $\left|\frac{1}{\sqrt{\left(\frac{1}{64}\right)+\left(\frac{1}{16}\right)+\left(\frac{1}{16}\right)}}\right|$

$=\left|\frac{1}{\sqrt{\left(\frac{9}{64}\right)}}\right|$

=$\frac{8}{3}$

So that the correct option is A.