The locus represented by $x y + y z = 0$ is

a pair of perpendicular lines

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a pair of parallel lines

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a pair of parallel planes

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a pair of perpendicular planes

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Solution

The correct option is D a pair of perpendicular planes
$x y + y z = 0$
$\Rightarrow y (x + z) = 0$
$\Rightarrow y = 0 or x + z = 0$
which represents a pair of planes whose dot product is zero.
Therefore, the equation represents a pair of perpendicular planes.

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Similar questions

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(d) a pair of perpendicular planes

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The locus represented by xy+yz=0 is

The correct option is D a pair of perpendicular planes xy+yz=0 ⇒y(x+z)=0 ⇒y=0 or x+z=0 which represents a pair of planes whose dot product is zero. Therefore, the equation represents a pair of perpendicular planes.

The locus represented by $x y + y z = 0$ is

The correct option is D a pair of perpendicular planes
$x y + y z = 0$
$\Rightarrow y (x + z) = 0$
$\Rightarrow y = 0 or x + z = 0$
which represents a pair of planes whose dot product is zero.
Therefore, the equation represents a pair of perpendicular planes.