Find the area of the parallelogram that has the given vectors u = i + j + k,      v = j + k as adjacent sides. Use a computer algebra system or a graphing utility to verify your result.

Find two vectors v, and u2 whose sum is (-2,-5), where is parallel to (-3, 4) while v2 is perpendicular to (3, 4).

Determine the angle, to the nearest degree, between the vectors = (5,3), b= (-1,–2)

Consider the following vectors: u = (1, −2, −1), v = (-2, 1, 8) Without using the cross product, find a vector n which is orthogonal to both u and U. You need to use a notion from chapter 5 to set up a system of linear equations, then use RREF to solve the system. Explain why this method works.