Problem 1. (13 points) The following problems will all consider the plane PQR, which is the unique plane through the non-colinear points P = (2,-1,2), Q = (3,0,-2), and R=(-1,1,0). (a) Give an equation for this plane. (b) Determine the angle between the given plane PQR and the plane defined by the equation 3x + 4y - 5z = 1. (c) Does the given plane PQR intersect the plane defined by the equation 3x + 4y - 5z = 1? If yes, give a paramterization of the intersection. If no, explain why. (d) A third plane is given by the equation A(x - 2) + B(y + 3) - 18(2-1) = 0, where A and B are unknowns find all of the values A and B for which this third plane is orthogonal to both the plane PQR and the plane defined by the equation 3x + 4y - 5z = 1. (e) Consider the vector-valued function r(t) = (3 cos(t), 5 sin(t), t2 2) i. Verify that r(t) intersects the plane PQR when t = 0. ii. Find the tangent line to r(t) at t = 0. (i.e. find the vector tangent at t = 0 and use this as a direction vector of your line). iii. Does the this tangent line lie on the plane, is it perpendicular to the plane, or is it neither. If it is neither, compute the angle between the line and the normal vector of PQR