a) For a point at latitude 61, longitude gbl on a sphere, What are the my and z components of the unit position vector describing this point? [1] b) Find the following integral: f 332 sina: dx. [2] c) Write down an expression for sin(30) in terms of sin 0. [2] d) Find the rst three nonzero terms in the Maclaurin series expansion of 62;\". [2] e) Find the mean value of cosx between 0 and 7T/ 2. [2] f) Find a vector that is perpendicular to [1,1,2] and [3,1,0]. [1] g) Give the equation for the unit vector parallel to [6,10,8]. [1] h) Given the function f (:13) = 6\"2, nd the :IJvalue of the maximum/minimum point and demonstrate Whether it is a maximum or a minimum. [3] i) Write down the equation of the plane passing through the points (5,1,0), (0,3,2) and (1,1,1). [2] [16 total]