=) Consider the following vectors: \vec{w}=\langle 3,-1\rangle \quad \text { and } \quad \vec{u}=\langle-4,2\rangle (a) (1 point) Use the dot product to show that w is not orthogonal to u.

Explain your answer (that is,explain why your dot product computation shows that w is not orthogonal to ū). (b) (2 points) Find the angle between w and ū. Give an exact answer (your answer should contain the inverse cosine function). (c) (2 points) Write the orthogonal decomposition of w along ü, that is, find w1 and w2 such that w = w1+ w2, w1 is parallel to ū, and w2 is orthogonal to ū. (d) (3 points) Write the orthogonal decomposition of u along w, that is, find u1 and u2such that ū = ũ1 + u2, u2 is parallel to w, and u2 is orthogonal to w.