1. You are given the following vectors in terms of their components in the i, j, k basis: A = i+ 2j-2k, B = 3i + j+2k, C=41- j+ k. (a) Show that these vectors are linearly independent, meaning that oA + BB + YC =0 if and only if a = B = y =0. (b) Compute A, B and C. (i.e., A = [A|, etc.) (c) Compute 2A + B, 3C - B, A + B + C 2. Use hyperbolic functions to compute the following integral: VI + 72 (1) (Hint: use the substitution a = sinh(t)) 3. prove that sinh(ir) and cosh(ir) are periodic functions (it's easier than you think!)