The place x-2 y+z=0 is parallel to the line

Step-by-step solution

A line with direction vector b = a i + b j + c k is parallel to a plane with normal vector n = A i + B j + C k if and only if n b = 0 . The normal vector to the plane x - 2y + z = 0 is n = 1 i - 2 j + 1 k . We check the dot product for each option: For (RUsrb), b = 4 i + 5 j + 6 k . n b = (1)(4) + (-2)(5) + (1)(6) = 4 - 10 + 6 = 0 . Since the dot product is zero, the line is parallel to the plane. We also check if the line lies in the plane by testing a point on the line, such as (3, 4, 3) . Substituting into the p