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`.

If theta is the angle between vec a = 2i-j+k and vec b = i+2j+k , then cos theta=

Given that vec A + vec B= vec R and A^(20 + B^(2) -R^(2) , find the angle between vec A and vec B .

If vec C=vec A+vec B then ((C)/(A))^(2)> 1+((B)/(A))^(2) is true for angle between vec A and vec B

If vec R = (vec A = vec B), show that R^(2) =A^(2) +B^(20 +2 AB cos theta wher, theta is the smaller angle between vec A and vec B .

If vec a+ vec b+ vec c= 0 , show that the angle theta between vec a and vec b is given by cos theta = c^2- a^2- b^2 / 2ab .

If theta is the angle between the unti vectors vec a and vec b , then proves that cos((theta)/(2)) = 1/2 |vec a + vec b| .

If theta is the angle between the unit vectors vec a and vec b , then prove that sin (theta)/(2) = 1/2|vec a - vec b|

If vec a and vec b are unit vectors and theta is the angle between them, show that (sin theta/2=1/2|vec a - vec b | .

If vec A and vec B are two non-zero vectors such that |vec A+vec B|=(|vec A-vec B|)/(2) and |vec A|=2|vec B| then the angle between vec A and vec B is theta such that cos theta=-(m)/(n) (where m and n are positive integers and (m)/(n) lowest form then find m+n