Let r(t)= asinti+j+acost k be a vector-valued function, where a is a non-zero constant and t 0.(a) Is r(t) perpendicular to r(t) for every t? Is r(t) perpendicular to r(t) for every t? Justify your answer in each case. [14 marks](b) Would the answers for part (a) remain the same regardless of how r was defined (i.e., if r was an arbitrary non-zero vector-valued function)? If yes, show why. If not, give a counterexample.