In the following cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(3, -2, 1) 2x - y + 2z + 3 = 0

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Solution

The equation of plane is 2x –y + 2z + 3 = 0
Let p be length of perpendicular from (3, -2, 1) on plane.

therefore space space space space space space straight p space space equals space fraction numerator 2 left parenthesis 3 right parenthesis minus left parenthesis negative 2 right parenthesis space plus space 2 space left parenthesis 1 right parenthesis space plus space 3 over denominator square root of left parenthesis 2 right parenthesis squared plus left parenthesis negative 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared end root end fraction space equals space fraction numerator 6 plus 2 plus 2 plus 3 over denominator square root of 4 plus 1 plus 4 end root end fraction space equals space fraction numerator 13 over denominator square root of 9 end fraction space equals 13 over 3

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