Question

Find the Cartesian equations of the line passing through A(2, 2, 1) and B(1, 3, 0).

Answer 1

The cartesian equations of the line passing through the points (x₁, y₁, z₁) and (x₂, y₂, z₂) are

`(x - x_1)/(x_2 - x_1) = (y - y_1)/(y_2 - y_1) = (z - z_1)/(z_2 - z_1)`

Here, (x₁, y₁, z₁) ≡ (2, 2, 1) and (x₂, y₂, z₂) ≡ (1, 3, 0)

∴ The required cartesian equations are

`(x - 2)/(1 - 2) = (y - 2)/(3 - 2) = (z - 1)/(0 - 1)`

i.e. `(x - 2)/(-1) = (y - 2)/(1) = (z - 1)/(-1)`.