Question

True or False?

The line through the points `(-3, 8,-4)` and `(1, 0, 8)` intersects the yz-plane at `(0,2,5)`.

Answer

True.

Line through the points `P=(-3,8,-4)` and `Q=(1,0,8)` is

`(x,y,z)=P+t(Q-P)=(-3,8,-4)+t(1-(-3),0-8,8-(-4))=`

`=(-3,8,-4)+t(4,-8,12)=(-3+4t,8-8t,-4+12t)`.

Line intersects the yz-plane when x-coordinate equals `0`, i.e. when `-3+4t=0`.

Thus, `t=3/4` and point of intersection is `(-3+4*3/4,8-8*3/4,-4+12*3/4)=(0,2,5)`.