Q115 / 180 · KCET 2024 · Mathematics

The equation $x y=0$ in three-dimensional space represents

  • A
    a pair of straight lines
  • B
    a plane
  • Correct answer
    C
    a pair of planes at right angles
  • D
    a pair of parallel planes

Solution

$\because x y=0$ $\Rightarrow \quad x=0$ or $y=0$ Hence, the locus of $x y=0$ is the union of all points. Which lie in $Y Z$-plane or on $Z X$-plane. So, the equation $x y=0$ represents a pair of planes at right angles.

Hence, the correct answer is option: 'C'.

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