Find the intersection of the line and plane: 2𝑥−4𝑦+𝑧=38, 𝐫(𝑡)=⟨2,−1,0⟩+𝑡⟨2,−2,−2⟩

Answer 1

The equation of the line can be written as x=2t+2, y=-2t-1 and z=-2t. Plugging this into the equation of the plane we obtain that 10t=30 or t=3. Hence, the intersection of the line and the plane is at the point (8,-7,-6).