(1) (10 pts) Consider three vectors A, B and C which has the following forms: A = Ari + Ajj + Azk, B = Bri + Byj + Bzk, C = Cri + Cyj + Czk Suppose we denote the vector sum of A, B and C as R. (a) (1 pts) We know that the resultant vector may be written in the form R = Rri + Ryj + Rzk. What are Rx, Ry, Rz in terms of the components of the vectors A, B and ? (b) (1 pts) Now, write expressions for the magnitudes | A|, | B), |C| and | R|. In terms of the components of the vectors A, B and C. (c) (3 pts) Based on what you have found in (b), show that in general, | R| # |A| + [B| + |CI. (d) (5 pts) Now, suppose that ALL the components of the vectors A, B and C' are EQUAL. Set this equal to R. ( That is, Ax = Ba = Ca = Ay = By =. ...= R) Prove now that in this case: | R) = [A| + |B) + |C)