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Given vectors a = h−2,−1,0i, b = h3,1,−2i and c = h1,−2,2i a) Find the angle between a and b .
b) Determine which (if any) of a , b and c are perpendicular to each other .
c) Calculate the projection of b onto a−c . d) Find (b−a)×c .
Question 2. 11+4=15 marks Consider the function y = sinx√12cosx + 23 on [0,π].
a) Show that
dy dx
=
18cos2 x + 23cosx−6 √12cosx + 23 .
Hence show that the function has a local maximum on [0,π] of
77 9√3.
b) Find the average value of y on [0,π].
