5. Let W be a plane that satisfies (a) Describe the plane in vector form, explaining your reasoning step by step. (b) Describe the plane in normal form, explaining your reasoning. (c) Pick two values of b and let W₁ and W₂ be the corresponding planes. Discuss how the two planes are different and similar. 3(x-1)+2(y+3)+2(z-2) = b, where b is a real number.

Find an equation for the plane containing the two (parallel) lines v (0, 1, -4) + t(1, 3, -5) and v, = (4, –1, 0) + t(1, 3, –5). %3D

3 4 33. Determine the vector equation, parametric equations, and, if possible, symmetric equation of the line that passes through the point P(1, 3, 5) and a. has direction vector (-2, -4, -10) b. also passes through the point Q(-7, 9, 3) c. is parallel to the line that passes through R(4, 8, -5) and S(-2, -5,9) d. is parallel to the .x-axis e. is perpendicular to the line (x, y, z) = (1, 0, 5) + (-3, 4, -6) f. is perpendicular to the plane determined by the points A(4, 2, 1), 4 2), and C(-3, 2, 1) nd 59 nsv of -3 of the plane that