Find the Cartesian equation of the plane passing through A( -1, 2, 3),

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

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

Answer»

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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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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