Let L be the line passing through the point P=(−3, −1, −5) with direction vector →d=[4, 0, 4]T, and let T be the plane defined by 4x−y−3z = 16. Find the point Q where L and T intersect.

Question

please help..

Answer 1

parametric equation of your line:
x = -3 + 4t
y = -1
z = -5 + 4t

sub those into the equation of the plane and solve for t
then get x, y, and z

Answer 2

x=7/4
y=15
z=1/12

is this correct?

Answer 3

or am I doing something wrong?

Answer 4

Sarah, I did not check back on your post til now, sorry

so sub back in:
4x - y - 3z = 16
4(-3 + 4t) - (-1) - 3(-5 + 4t) = 16
-12 + 16t + 1 + 15 - 12t = 16
4t = 12
t = 3

x = -3+12=9 , y = -1, z =-5+12 = 7
so the point of intersection is (9,-1,7)

I have no idea how you got your answer