SECTION B 3 (a) The 3 non-zero vectors (in 3-dimensional space) a, b, c satisfy a =boc, b=c0a, c= a lib. Evaluate la| + b|+ c- (6 marks) In Questions 3(b) and 3(c), Cartesian coordinates are denoted by the usual symbolsx, y and z . (b) Evaluate the line integral [(3x-2,/y + z)ds, where C is the portion of the curve x = t + bt, y =t and z=bt-2t from the point (2+2b, 4, 2b-4) to the point (4+4b, 16, 4b - 8). Here bis a constant. Give your answer in terms of b. (6 marks) (c) Consider the force field F = [ yz- y sin( x y)li + [ xz-x sin( x y)]j + xyk . Find a potential function _( X,y,z) for the vector function F. If C is any path from point P (1, 0. 1) to point Q (4, #/4, 3), evaluate the work done Wby the force to push an object from point P to Q: W= [. dr