Find the point at which the line

Question

Find the point at which the line ⟨1,−2,1⟩ + t⟨−1,5,1⟩ intersects the plane −x−4y−z=−74.

( , , )

Answer 1

Find the point at which the line ⟨1,−2,1⟩ + t⟨−1,5,1⟩ intersects the plane −x−4y−z=−74.

Parametric equation of line: x = 1 - t; y = - 2 + 5t; z = 1 + t.

To get intersection point: - 1 + t + 8 - 20t - 1 - t = - 74; - 20t = - 80; t = 4

x = - 3; y = 18; z = 5.

(-3, 18, 5) is intersection point.