Consider the vectors a = 6i + 7j + 6k and b = 4i – j+ 8k, where i, j, and k are mutually- perpendicular unit vectors forming a right-handed system. (a) Calculate (i) a + b. (ii) The magnitude |a| of a. (iii) The unit vector b in the direction of b. (iv) The scalar product a · b. (v) The vector product a x b. (vi) The direction cosines of a. (vii) The angle between a and b, expressed in degrees to two decimal places.