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Find the Cartesian equation of the plane passing through A( -1, 2, 3), the direction ratios of whose normal are 0, 2, 5.

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The cartesian equation of the plane passing ; through (x1, y1, z1), the direction ratios of whose normal are a, b, c, is

a(x – x1) + b(y – y1) + c(z – z1) = 0

∴ the cartesian equation of the required plane is

0(x +1) + 2(y – 2) + 5(z – 3) = 0 

i.e. 0 + 2y – 4 + 5z – 15 = 0 

i.e. 2y + 5z = 19.

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