Question

The three planes $x+y=0,y+z=0$ and $x+z=0$

• A. meet in a unique point
• B. meet in a line
• C. meet taken two at a time in parallel lines
• D. None of these

Answer 1

Answer: (A)

The planes $x+y=0$
i.e. $x=-y$ and $y+z=0$
i.e. $z=-y$ meet in the line
$\frac{x}{l}=\frac{y}{-1}=\frac{z}{1}$.
Any point on this line is $(t,-t,t)$.
This point lies in the plane $x+z=0$
if $t+t=0\Rightarrow t=0$
So the three planes meet in a unique point $(0,0,0)$.