The vector equation of plane in parametric form, passing through the points (-1, 2, 0), (2, 2, -1) and parallel to the line x-1 1 = 2y+1 2 = z+1 -1 is

Step-by-step solution

The position vector of the point A(-1, 2, 0) is a = - i + 2 j . The plane passes through A(-1, 2, 0) and B(2, 2, -1) . A vector parallel to the plane is AB = (2 - (-1)) i + (2 - 2) j + (-1 - 0) k = 3 i - k . The given line is x-1 1 = 2y+1 2 = z+1 -1 . Rewriting it in standard form, we get x-1 1 = y+1/2 1 = z+1 -1 . The direction vector of the line is v = i + j - k . Since the plane is parallel to this line, v is also parallel to the plane. The parametric vector equation of a plane passing through a point with posit