Question

The equation of a plane having equal intercepts on coordinate axes and is unit distance from $(1,2,-3)$ can be ?

• A. $x+y+z=3$
• B. $x+y+z=\sqrt{3}$
• C. $x+y+z=-\sqrt{3}$
• D. $x+y+z=-3$

Answer 1

Answer: (B), (C)

$x+y+z=-\sqrt{3}$

Equation of plane have equal intercept $a$:
$\frac{x}{a}+\frac{y}{a}+\frac{z}{a}=1\Rightarrow x+y+z=a$
Now, distance from $(1,2,-3),$
$1=\left|\frac{1+2-3-a}{\sqrt{3}}\right|\Rightarrow a=\pm \sqrt{3}$
So, equation of plane can be : $x+y+z=\pm \sqrt{3}$