Q1) Let a = (1, 3, 5, -2), b = (1,0, -1, 2) and c = (-2, -4, -1, 2) be vectors in R4. Part (a) [4 points]: Find (a . c)b + ||2c|la. Part (b) [6 points]: Find two perpendicular vectors p and q in IR* such that their sum is the vector b and such that p is parallel to a. Part (c) [3 points]: If T(4, 3, 2, 1) is the terminal point of the vector a, then what is its initial point? Part (d) [2 points]: Find a vector in R* that is perpendicular to b. Q2) Consider the following planes II1 : 9x + 15y + 21z = 1, I12 : 6x + 10y + 14z = 2. Part (a) [3 points]: Show that planes II, and II2 are parallel. Part (b) [5 points]: Find the distance between the planes II, and II2. Q3) Compute the vector x x y where x = (5, 4, 3) and y = (1, -1, -3). Q4) Suppose that m and n are two vectors in R2021 such that | |m + n| | = 2 and | |m - n)| = 4. Determine whether the angle between m and n is acute, right, or obtuse. Q5) Suppose that u and v are two perpendicular vectors in R 2 such that | |u| | = 3 and | |utv|| = 6. Find the magnitude of v