Question

Find an equation of the described plane. (a) The plane through the point (2,3,4) and parallel to the plane 3x-y +7z = 8
(b) The plane through the points (5,3, 8), (6,4,9) and (3,3,3)
(c) The plane that passes through the line of intersection of the planes x-z = 1 and y + 2z = 3 and is perpendicular to the plane z+y-2z = 1.
(d) The plane that passes through the point (5,7,3) and contains the line x(t) = t₁ y(t) = t, z(t) = t. (Hint: First find another line on the plane with the point (5,7,3) and a point on the given line.)