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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.
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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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