Q75 / 180 · KCET 2018 · Mathematics
The locus represented by \( x y+y z=0 \) is
- AA pair of perpendicular lines
- BA pair of parallel lines
- CA pair of parallel planes
- Correct answerDA pair of perpendicular planes
Solution
Given the locus
\[ \begin{array}{l} x y+y z=0 \\ \Rightarrow y(x+z)=0 \\ \Rightarrow \vec{y} \cdot(\vec{x}+\vec{z})=0 \end{array} \]
Therefore, it represents a pair of perpendicular planes.
\[ \begin{array}{l} x y+y z=0 \\ \Rightarrow y(x+z)=0 \\ \Rightarrow \vec{y} \cdot(\vec{x}+\vec{z})=0 \end{array} \]
Therefore, it represents a pair of perpendicular planes.
Hence, the correct answer is option: 'D'.