If angle between $\overrightarrow{a}and\overrightarrow{b}is\frac{\pi }{3},$ then angle between $2\overrightarrow{a}and-3\overrightarrow{b}$ is

Step 1: Draw vector a and b    [Ref. Fig.1]
 

Step 2: Draw  2a and −3b          [Ref. Fig.2]

Vector 2a will be twice the length of a in the same direction.

Vector −3b will be of thrice the size of vector b but in opposite direction.

Let ϕ be the angle between 2a and −3b.

    $\varnothing =\mathrm{\pi }-\mathrm{\pi }/3=2\mathrm{\pi }/3$
 

Hence, Angle between 2a and −3b is $2\mathrm{\pi }/3$​.