Question

The locus represented by $xy+yz=0$ is

• A. A pair of perpendicular lines
• B. A pair of parallel lines
• C. A pair of parallel planes
• D. A pair of perpendicular planes

Answer 1

Answer: (D)

$xy+yz=0$
$y(x+z)=0$
$\Rightarrow y=0$ and $(x+z)=0$
$\Rightarrow y=0$ is a equation of $xz$-plane.
$\Rightarrow x+z$ is also an equation of plane.
$d$.$r^{\prime }$.$s$ of normal to the plane $y=0$ is $(0,1,0)$ and $d$.$r^{\prime }$.$s$ of normal to the plane $x+z=0$ is $(1,0,1)$
Now, $a_1{a}_2+b_1{b}_2+c_1{c}_2=0\times 1+1\times 0+0\times 1=0$
Hence, both planes are perpendicular.