If ` vec R = vec A- vec B` , and ` theta` is the smaller angle between ` vec A ` and ` vec B` , show that ltbRgt ` R^2 = A^2 + B^2 -2 AB cos theta`.

Explanation

Given, ` vec R = vec A- vec B= vec A+ (- vec B),
As ` theta` is the angle between ` vec A ` and ` vec B` , therefore,
angle betwwen ` vec A` and ` vec -B` is ( 180^2-theta)`. Using prarallelogram law of vectrs addition ltbRgt or ` R^2 =A^2 + B^2 + 2 AB cos ( 180^2- theta)`
` = A^2 + B^2 -2 AB cos theta` .