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.
$d$.$r'$.$s$ of normal to the plane $y = 0$ is $(0, 1, 0)$ and $d$.$r'$.$s$ of normal to the plane $x + z = 0$ is $(1, 0, 1)$
Now, $a_1a_2 + b_1b_2 + c_1c_2 = 0 \times 1 + 1 \times 0 + 0 \times 1 = 0$
Hence, both planes are perpendicular.