Calculus dot product question

given a and b unit vectors, if the angle between them is 60degree calculate (6a+b) * (a-2b)

thx

Using distributivity and commutativity of dot product we have
(6a+b) • (a-2b) = 6a•a-11a•b-2b*b
Since a and b are unit vectors, the dot products a•a and b•b are both equal to 1. Since the angle between a and b is 60 degrees, a•b equals the product of the norms of a and b and the cosine of this angle which is 1/2. Therefore a•b=1/2. Plugging in the above expression we get
(6a+b) • (a-2b) = 6-11/2-2=-3/2.

a • b = |a| |b| cosθ

<6a, b> • = √((6a)² + (b)²) * √((a)² + (-2b)²) * cos(60°)
<6a, b> • = √(36a² + b²) * √(a² + 4b²) * ½
<6a, b> • = ½ √[(36a² + b²) (a² + 4b²)]
<6a, b> • = ½ √[36a^4 + 145a²b² + 4b^4]