The resultant of 2 vectors A & B is at right angles to vector A and its magnitude is half of vector B. Find the angle between vectors A & B ?

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

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Ramesh