Determine if the line (𝑙) and the plane (𝛼)are parallel or perpendicular. (𝛼):2𝑥+𝑦−2𝑧=3 (𝑙): x=2t+1, y=-2t-2, z=t+1

Answer 1

Vector <2, - 2, 1> is direction vector of this line. Vector <2, 1, - 2> is normal vector of this plane.

We see that this vectors not parallel, because coordinates not proportional, but this vectors perpendicular because their dot-product <2, - 2, 1> • <2, 1, - 2 > = 4 - 2 - 2 = 0. So given line (l) parallel to given plane (α)