KCET · Maths · Three Dimensional Geometry
The equation \(x y=0\) in three-dimensional space represents
- A a pair of straight lines
- B a plane
- C a pair of planes at right angles
- D a pair of parallel planes
Answer & Solution
Correct Answer
(C) a pair of planes at right angles
Step-by-step Solution
Detailed explanation
\(\because x y=0\)
\(\Rightarrow \quad x=0\) 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.
\(\Rightarrow \quad x=0\) 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.
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