inner products T a u v where u 12 T v 5 b x y where x 10 14 3 y 0 49 00 c 2u v v using u and u above Compute the norms of u v x and y above simplify only where reasonable Compute the distance from u to v above Find the angle between u and u above calculator needed Draw two vectors in R2 which are not perpendicular Verify this by showing that a their dot product nonzero and b the Pythagorean for dot products does not hold for these vectors Prove that the standard dot product we re using actually satisfies all of the properties of an inner produc