Question

A(-2, 3, 4), B(1, 1, 2) and C(4, -1, 0) are three points. Find the Cartesian equations of the line AB and show that points A, B, C are collinear.

Answer 1

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

Here, (x₁, y₁, z₁) = (-2, 3, 4) and (x₂, y₂, z₂) = (4, -1, 0)

∴ the required cartesian equations of the line AB are

∴ coordinates of C satisfy the equations of the line AB. 

∴ C lies on the line passing through A and B. Hence, A, B, C are collinear.