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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.
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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