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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 -- Ramesh
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
--
Ramesh
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