Question

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

Answer 1

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.