Question

The distance of the point $(1,-5,9)$ from the plane $x-y+z=5$ measured along the line $x=y=z$ is:

• A. $3\sqrt{10}$
• B. $10\sqrt{3}$
• C. $\frac{10}{\sqrt{3}}$
• D. $\frac{20}{3}$

Answer 1

The correct option is B $10\sqrt{3}$

Equation of the line

$\frac{x-1}{1}=\frac{y+5}{1}=\frac{z-9}{1}=\lambda$

The co -ordinates of the point is $(\lambda +1,\lambda -5,\lambda +9)$

Substitute the co-ordinates in the equation of the plane

$x-y+z=5$

$\lambda +1-\lambda +5+\lambda +9=5$

$\lambda =-10$

One point $=(1,-5,9)$

Other point $=(-9,-15,-1)$

Distance between the two points $=\sqrt{(-9-1{)}^2+(-15+5{)}^2+(9+1{)}^2}=\sqrt{100+100+100}=10\sqrt{3}$