SOLUTION: Find the point at which the line ⟨−5,−5,−2⟩+t⟨5,3,−2⟩ intersects the plane 5x+3y+2z=16

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Find the point at which the line ⟨−5,−5,−2⟩+t⟨5,3,−2⟩ intersects the plane 5x+3y+2z=16      Log On


   

Question 1073909: Find the point at which the line ⟨−5,−5,−2⟩+t⟨5,3,−2⟩ intersects the plane 5x+3y+2z=16
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
x=-5%2B5t
y=-5%2B3t
z=-2-2t
Substitute into the plane equation,
5%28-5%2B5t%29%2B3%28-5%2B3t%29%2B2%28-2-2t%29=16
-25%2B25t-15%2B9t-4-4t=16
30t-44=16
30t=60
t=2
Now that you know t, go back and find x, y, and z.
I'll leave that to you.