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

[fk378]

Homework Statement

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

Homework Equations

r= r_0 + tv

The Attempt at a Solution

The line through A and B is the vector AB and can be found by subtracting the A components from the B components. So B-A= <3,-2,1>.

They give x+y+z=6 so the components of that vector is <1,1,1>.

Not sure where to go from here...

 

[Dick]

Put the components of your parametric equation for the line, e.g x=1+3t into the equation for the plane and solve for t, please? The normal vector to the plane doesn't have much to do with it.