If a and b are unit vectors, and |a-b|=5, evaluate (2a+5b) . (3a-4b).

Ok, so can someone please check my work for me? I am just not sure on one part, finding the angle of cos(theta). Btw this is the dot product.

a and b both have u-hats on them

6(a)^2 + 7(a)(b)-20(b)^2

=6(1)^2+7(0.5)-20(1)^2

=-10.5

dot product work:

a . b = |a||b|cos(theta)

=(1)(1)cos60

=0.5

I was wondering if I had my angle theta correct

To get it, I used the cos law,

so theta is the angle across from 1 in my diagram.. am I supposed to look for the angle between a and b or between a and a-b.. Because I looked for the one between a and a-b

cos(theta)=(1+5-1)/(2(1)(5))

theta=0.5