The locus represented by xy + yz = 0 is | vedclass

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(D) The given equation is $xy + yz = 0$. Factoring out $y$,we get $y(x + z) = 0$. This equation is satisfied if $y = 0$ or $x + z = 0$. In $3D$ space,

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$A$ pair of perpendicular planes

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(D) The given equation is $xy + yz = 0$. Factoring out $y$,we get $y(x + z) = 0$. This equation is satisfied if $y = 0$ or $x + z = 0$. In $3D$ space,$y = 0$ represents the $xz$-plane and $x + z = 0$ represents a plane passing through the $y$-axis. The normal vectors to these planes are $\vec{n_1} = (0, 1, 0)$ and $\vec{n_2} = (1, 0, 1)$. The dot product of the normal vectors is $\vec{n_1} \cdot \vec{n_2} = (0)(1) + (1)(0) + (0)(1) = 0$. Since the dot product of the normal vectors is $0$,the planes are perpendicular. Therefore,the locus represents a pair of perpendicular planes.

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

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