Question

Find the point of intersection of the line `(x + 1)/2 = (y - 1)/3 = (z - 2)/1` with the plane x + 2y – z = 6.

Answer 1

`(x + 1)/2 = (y - 1)/3 = (z - 2)/1` = r  ...(say)

∴ Coordinates of any point on this lines are (2r – 1, 3r + 1, r + 2)

This point lies on the plane x + 2y – z = 6

∴ (2r – 1) + 2(3r + 1) – (r + 2) = 6

∴ 2r – 1 + 6r + 2 – r – 2 = 6

∴ 7r = 7

∴ r = 1

∴ Point of intersection = (1, 4, 3)