The two vectors a and b lie in the xy plane and make angles α and β with the x axis.
a)By evaluating a • b in two ways (Namely a •b = abcos(θ) and a • b = a1b1+a2b2) prove the well-known trig identity
b)By similarly evaluating a X b prove that
sin(α-β) = sin(α)cos(β) - cos(α)sin(β)
c)Now let vector a make an angle -α with the x axis and find a similar expression for
a • b = abcos(θ)
a • b = a1b1+a2b2
The Attempt at a Solution
I drew the vectors a and b with their appropriate angles to the x-axis... The angle between the vectors is (α-β) so I have a •b = abcos(α-β) but I have no idea how to relate this to the trig identities!