Let a = (4, 5, 3} and b = {[1, 5,4)_ Show that there are scalars s and t so that as + th = (4, 15, 5} You might want to sketch the 1v.rs:ctt::rs to get some intuition. 5=| | t= I: il Suppose E = {2, 1) and E = {1, 7) are two vectors that form the sides of a parallelogram. Then the lengths of the two diagonals of the parallelogram are Separate answers with a comma. Find two 1rr'elzmrs 51 and 5: whose sum is (1, 5}, where 51 is parallel to (3, 2) while E1. is perpendicular to (3, 2}_ 51 I land 5| || Let a, b, c and y be the three dimensional vectors a =4j +3k, b = -51+4j+7k, c=4i+7j, y=4i+5j Perform the following operations on these vectors: (ajc . ata . y = (b) (a . b) a = (c) ((c . c)a) . a =