4. Show how to find the equation of the plane which contains the points P(1, 2, 3), Q(-2, 0, 4) and R(5, -1, 1).2. In each case, give a vector equation for a line satisfying the given conditions. a) contains (3,4, 2) and is parallel to the line r(t) = (7 t, 5 + 0.5t, 3> b) contains (1,2,3) and (6,4, 1) c) contains (2, 0.33, J27) and is perpendicular to the plane 2.1: y 52 = 10 3. Draw the triangular piece of the plane 21 + y + 32 = 12 which lies in the rst octant. In your drawing, label the plane's 3-, y- and z-interoepts with their coordinates. 1. Let v = (1, 2, 2) = i + 2j + 2k and w = (3, 1, -4) = 3i + j - 4k. a) Find v. w. What does the sign of this answer tell us about the angle between v and w? b) Find the angle between v and w. Give an exact answer involving v and cos-1. c) Find v x w. What is the angle between v x w and v? d) Find v x w . What does this answer represent geometrically