In the following cases, find the distance of each of the given points from the corresponding given plane.
Point Plane
(0, 0, 0) 3 x - 4 y+12 z = 3

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Solution

The equation of plane is 3x – 4y+ 12 z – 3 = 0
Let p be length of perpendicular from (0, 0, 0) on plane.

therefore space space space space space space space straight p space equals space fraction numerator open vertical bar 3 space left parenthesis 0 right parenthesis space minus 4 left parenthesis 0 right parenthesis space plus space 12 space left parenthesis 0 right parenthesis space minus space 3 close vertical bar over denominator square root of left parenthesis 3 right parenthesis squared plus left parenthesis negative 4 right parenthesis squared plus left parenthesis 12 right parenthesis squared end root end fraction space equals fraction numerator open vertical bar 0 minus 0 plus 0 minus 3 close vertical bar over denominator square root of 9 plus 16 plus 144 end root end fraction space equals space fraction numerator open vertical bar negative 3 close vertical bar over denominator square root of 169 end fraction space equals 3 over 13

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