(Camera Models- 30 points) Prove that the vector from the viewpoint of a pinhole camera to the vanishing point (in the image plane) of a set of 3D parallel lines is parallel to the direction of the parallel lines. Please show steps of your proof. Hint: You can either use geometric reasoning or algebraic calculation. If you choose to use geometric reasoning, you can use the fact that the projection of a 3D line in space is the intersection of its "interpretation plane" with the image plane. Here the interpretation plane (IP) is a plane passing through the 3D line and the center of projection (viewpoint) of the camera. Also, the interpretation planes of two parallel lines intersect in a line passing through the viewpoint, and the intersection line is parallel to the parallel lines. If you select to use algebraic calculation, you may use the parametric representation of a 3D line: P = P0 +tV, where P= (X,Y,Z)T is any point on the line (here T denote for transpose), P0 = (X0,Y0,Z0)T is a given fixed point on the line, vector V = (a,b,c)T represents the direction of the line, and t is the scalar parameter that controls the distance (with sign) between P and P0.