Equation of a line/plane

fk378

1. The problem statement, all variables and given/known data
Where does the line through A(1,0,1) and B(4,-2,2) intersect the plane x+y+z=6?


2. Relevant equations
r= r_0 + tv


3. 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.