In the following cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(–6, 0, 0) 2x - 3y + 6z - 2 = 0

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Solution

The equation of plane is
2x – 3y + 6z –2 = 0
Let p be length of perpendicular from (– 6, 0, 0) on plane.

therefore space space space space space space space space space space space space space space space space space space straight p space space equals space fraction numerator open vertical bar 2 space left parenthesis negative 6 right parenthesis minus space 3 space left parenthesis 0 right parenthesis space plus space 6 space left parenthesis 0 right parenthesis space minus space 2 close vertical bar over denominator square root of left parenthesis 2 right parenthesis squared plus left parenthesis negative 3 right parenthesis squared plus left parenthesis 6 right parenthesis squared end root end fraction space equals space fraction numerator open vertical bar negative 12 minus 0 plus 0 minus 2 close vertical bar over denominator square root of 4 plus 9 plus 36 end root end fraction

fraction numerator equals space open vertical bar negative 14 close vertical bar over denominator square root of 49 end fraction space equals space 14 over 7 space equals space 2

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