Let L be the line passing through the point P=(1, −1, −5) with direction vector →d=[−2, −4, 3]T, and let T be the plane defined by −x+y−3z = −1. Find the point Q where L and T intersect.

Question

Let L be the line passing through the point P=(1, −1, −5) with direction vector →d=[−2, −4, 3]T, and let T be the plane defined by −x+y−3z = −1. Find the point Q where L and T intersect.

Reiny · Accepted Answer

parametric equations of the line L
x = 1 - 2t
y = -1 - 4t
z = -5+ 3t

plug those values into
-x + y - 3z = -1 and solve for t

once you have t, sub it back into the parametric equations to get the (x,y,z)

shana · Answer

Thank you so much