MHT CET · Maths · Three Dimensional Geometry
The foot of the perpendicular drawn from the origin to the plane is \((4,-2,5)\), then the Cartesian equation of the plane is
- A 4x-2y+5z=45
- B -4x+2y+5z=45
- C 4x-2y+5z+45=0
- D 4x+2y-5z+45=0
Answer & Solution
Correct Answer
(A) 4x-2y+5z=45
Step-by-step Solution
Detailed explanation
Substitute \(x=4, y=-2, \mathrm{z}=5\) in all options.
\(\therefore \quad\) For option A
\(\begin{aligned}
4 x-2 y+5 z & =4(4)-2(-2)+5(5) \\
& =16+4+25 \\
& =45
\end{aligned}\)
\(\therefore \quad\) Only option A is satisfied by \((4,-2,5)\)
\(\therefore \quad\) For option A
\(\begin{aligned}
4 x-2 y+5 z & =4(4)-2(-2)+5(5) \\
& =16+4+25 \\
& =45
\end{aligned}\)
\(\therefore \quad\) Only option A is satisfied by \((4,-2,5)\)
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