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].

2018-03-05
Maths