In the following cases, find the distance of each of the given points from the corresponding given plane. (2,3,−5) x + 2y − 2z = 9.

Engineering

Mathematics

Distance from a Plane

Question

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Comparing with Ax + By + Cz = D

A = 1, B = 2 C = –2, D = 9

Now,

Disatnce of the point from the plane

$= |\frac{(1 \times 2) + (2 \times 3) + (- 2 \times - 5) - 9}{\sqrt{1^{2} + 2^{2} + (- 2)^{2}}}|$

$= |\frac{2 + 6 + 10 - 9}{\sqrt{1 + 4 + 4}}|$

$= |\frac{18 - 9}{\sqrt{9}}|$

$= \frac{9}{3}$

= 3