MHT CET · Maths · Three Dimensional Geometry
The Cartesian equation of the plane passing through the point A \((7,8,6)\) and parallel to the XY plane is
- A \(z=1\)
- B \(y=8\)
- C \(x=7\)
- D \(z=6\)
Answer & Solution
Correct Answer
(D) \(z=6\)
Step-by-step Solution
Detailed explanation
The required plane passes through the point \((7,8,6)\) and is parallel to XY plane.
\(\therefore\) It is perpendicular to \(\mathrm{z}\) axis and direction ratios of \(\mathrm{z}\) axis are \(0,0,1\).
\(\therefore\) Required equation of plane is
\(
0(\mathrm{x}-7)+0(\mathrm{y}-8)+1(\mathrm{z}-6)=0 \Rightarrow \mathrm{z}=6
\)
\(\therefore\) It is perpendicular to \(\mathrm{z}\) axis and direction ratios of \(\mathrm{z}\) axis are \(0,0,1\).
\(\therefore\) Required equation of plane is
\(
0(\mathrm{x}-7)+0(\mathrm{y}-8)+1(\mathrm{z}-6)=0 \Rightarrow \mathrm{z}=6
\)
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