Determine [3a-4b].[2a+b], given a and b are unit vectors and the angle between them is 30 degree.

We'll determine the dot product of a and
b:

a*b = |a|*|b|*cos 30 =
1*1*sqrt3/2

We'll use FOIL method to remove the
brackets:

(3a-4b)(2a+b) = 3a^2 + 3ab - 8ab -
4b^2

The angle made by the vector a with itself is of 0
degrees.

a^2 = a*a = |a|*|a|*cos 0 = 1*1*1 =
1

b^2 = b*b = 1

(3a-4b)(2a+b)
= 6 + 3*sqrt3/2 - 8sqrt3/2 - 4

We'll combine like
terms:

(3a-4b)(2a+b) = 2 -
5sqrt3/2

The requested value of the product
is (3a-4b)(2a+b) = 2 - 5sqrt3/2.