Question

Find the points of intersection of the line x = 3 + 2t, y = 5 + 8t, z = −6 + t, that is, l(t) = (3 + 2t, 5 + 8t, −6 + t), with the coordinate planes. xy plane (x, y, z) = xz plane (x, y, z) = yz plane (x, y, z) =

Answer 1

See, please, suggested decision:
When the line intersects the xy-plane, then parameter z=0, when does the xz - y=0 and when does yz, x=0. All the details are in attachment.
If it's possible, check arithmetic part.