Question

the resultants of two vector A and B is at right angle to vector A and its magnitude is half of vector B.Find angle between vector A and B.

Answer 1

Let the vectors be A and B and the resultant be R and their magnitides be a,b,r and  let angle btn A and b be x

so A + B = R

also b2 = a2+ r2 ( from figure )

as r = b/2 we have a = 0.86 b

also angle between A and R is 90 , so dot product is zero

A.R=0 or A.(A+B)=0

as A.A = a2.cos 0 = a2

so A.B = - a2

and A.B = a*b*cos x

so cos x = -a2 /ab = -0.86

x=150 degrees