Question

Where does the line through (1,0,1) and (4,-2,2) intersect the plane x+y+z=6?

Answer 1

we should first define the line in a more vector form

Answer 2

what do you get when you subtract the components of one point from the other? this will give us a vector to work from

Answer 3

using one of the points (Xxo,yo,zo) and the vector between then <a,b,c>
\[x=x_0+at\]\[y=y_0+bt\]\[z=z_0+ct\]

these can be substituted into the x y and z parts of the plane to solve for t

which can then be used in the vector line setup to solve for the specific xyz parts of the point of intersection

Answer 4

Ah I get it now thanks! :]