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