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Question
Find the cartesian equation of the plane passing through A(1, 2, 3) and the direction ratios of whose normal are 3, 2, 5.
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Solution
The plane passes through the point A(1, 2, 3) and the direction ratios of it’s normal are 3, 2, 5.
∴ x1 = 1, y1 = 2, z1 = 3, a = 3, b = 2, c = 5
Equation of a plane in Cartesian form is
a(x – x1) + b(y – y1) + c(z – z1) = 0
∴ 3(x – 1) + 2(y – 2) + 5(z – 3) = 0
∴ 3x + 2y + 5z – 22 = 0
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