For the given vectors a and b (see the figure below), construct the following vectors: a + 1/2 b; 2a - b; 1/2b - 2a. (Draw neat diagrams; label vectors appropriately). (a) Find the initial point of the vector that is equivalent to vector u = (1, 2) and whose terminal point is B(2, 0). (b) Find the terminal point of the vector v = (1, 1, 3) and whose initial point is A(0, 2, 0). Find all scalars c_1, c_2, and c_3 such that c_1 (-1, 0, 2) + c^2(2, 2, -2) + c_3(1, -2, 1) = (-6, 12, 4) Evaluate the given expression with u = (-2, -1, 4, 5), v = (3, 1, -5, 7) and w = (-6, 2, 1, 1). (a) ||u||-2||v||-3||w|| (b) ||u||+||-2v||+||-3||M|| (a) || ||u-v||w|| Vectors u = (1, -3, 3); nu = (2, 3, 4) are given. Find an angle between u and nu - u. It is given: ||m|| = 4; ||n|| = Squareroot 3; (m, n) = 150 degree. (b) Find the norm of the vector m + 2n. (c) Determine if the vectors (m + 2n) and (-m + n) are orthogonal.