Question

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

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 

o(x + 1) + 2(y + 2) + 5(z – 3) = 0 

i.e. 0 + 2y – 4 + 10z – 15 = 0 

i.e. y + 2 = 0.