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

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Solution

The equation of plane is
x + 2y – 2 z – 9 = 0
Let p be length of perpendicular from (2, 3, -5) on plane.

therefore space space space space space space space space space space space straight p space equals fraction numerator 2 plus 2 left parenthesis 3 right parenthesis space minus space 2 left parenthesis negative 5 right parenthesis space minus space 9 over denominator square root of left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared plus left parenthesis negative 2 right parenthesis squared end root end fraction space equals space fraction numerator 2 plus 6 plus 10 minus 9 over denominator square root of 1 plus 4 plus 4 end root end fraction space equals fraction numerator 9 over denominator square root of 9 end fraction space equals 9 over 3 space equals 3

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