Question

Find the cartesian equation of a line passes through the point (- 2, 4, -5) and is parallel to (x + 3)/3 = (y - 4)/5 = (z + 8)/6.

Answer 1

Let line passes through point (x₁, y₁, z₁) whose dc’s are a,b,c then equation of line is

(x - x₁)/a = (y - y₁)/b = (z - z₁)c

Here line passes through (-2, 4, -5) and parallel to

(x + 3)/3 = (y - 4)/5 = (z + 8)/6

∴ dc's of the required line are 3, 5, 6.

Hence equation of line is

(x + 2)/3 = (y - 4)/5 = (z + 5)/6