Perpendicular Planes

[sxg133]

Plane P is given by the equation 3x+4y+5z=1.

Line L denotes the line parameterized by <0,1,-1> + t<-5,1,3>.

If Q is a plane perpendicular to P containing L, find a normal form for Q:
ax +by + cz = 1 or ax +by + cz = 0.

Can anyone help me with this problem?

 

[pka]

If n=<3,4,5> and m=<−5,1,3> then n×m=<7,−34,3>
Now the point T0,1,−1) is on L so it must be in plane Q.
You should put all that together.