Question

Show that the lines (x - 1)/3 = (y - 1)/-1 = (z + 1)/0 and (x - 4)/2 = (y/0) = (z + 1)/3 intersect and hence find the point of intersection.

Answer 1

The condition for intersecting is 

Any point on this line is of the form (2µ + 4, 0, 3µ – 1) Since they are intersecting, for some λ, µ 

(3λ + 1, – λ + 1,- 1) = (2µ + 4, 0, 3µ – 1) ⇒ λ = 1 and µ = 0 

To find the point of intersection either take λ = 1 or µ = 0 

∴ The point of intersection is (4, 0, – 1),