16. [Shadows] Consider the line segment between the points (1, 2. 3) and (2. 0, 2). n a (a) Give a parametrization of the line segment. and calculate its length. (1)) A light source is at the point (0,0,6), which casts a shadow of the line segment onto the :t'y-plane (the shadow will also be a line segment). Give a parametrization of the shadow. and calculate the length of the shadow. 17. [Shadows] Consider the parallelogram surface whose vertices are (0.0.1), (2.0.1), (3,2,1). and (1.2.1). A light source is at the point (0. l.2). which casts a shadow of the parallelogram onto the :y-plane. (The shape of the shadow will also be a parallelogram.) What is the area of the shadow? 18. [Shadow] Consider the segment of the curve parametrized by (t. 2.13) where 0 S t S 2; this curve is called a twisted cubic. A light source is at (-5.0. 10) casts a shadow of the twisted cubic onto the plane 1 - y = 5. Our goal will be to find a parametrization of the shadow. (a) Let t] he a constant with 0 S q S 2 so that r(q) = (q, 112.113) is an arbitrary point on the twisted cubic; parametrize a ray which starts at the light source and goes through this point. Use T as the permueter for this parametrization; the parametrization will also have q as a constant. (Note: T is a different variable from t.) (b) Plug your answer from part (a) into the equation of the plane and solve for T: this will tell you the parameter for when the ray hits the plane. (c) Plug your answer from part (b) back into the equation of the ray; this will tell you the position of the shadow of each point on the curve. Your answer will still have q, but we can now think of q as a parameter