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# CBSE Class 11-science Answered

two vectors A and B have equal mag itudes.if magnitudes of A+B is equal to n times the magnitude of A-B.What is the angle between A andB?

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Asked by ABHILASHA | 05 Aug, 2019, 08:53: PM Expert Answer
( Vectors are tyoed in Bold, i and j are unit vectors along x and y direction respectively )

Let A = a i   and  B = b i + c j

since A and B are vectors of equal magnitude, we have,  a2 = b2 + c2 = m  ....................(1)

A + B  = (a+b) i + c j  .....................(2)
A - B = (a-b) i - c j ...........................(3)

magnitude of ( A+B ) is n times magnitude of (A-B)

Hence (a+b)2 + c2  = n2 [ ( a-b )2 + c2 ] ........................(4)

a2 + b2 + c2 + 2ab = n2 [ a2 +b2 + c2 - 2ab ] ...................(5)

by using eqn.(1) and after simplification, eqn.(5) is written as,   m(n2 -1) = ab (n2 + 1 )  ...............(6)

Angle θ between A and B ;- ........................(7)
from eqn.(6) and (7), we get cosθ = (n2 - 1) / (n2 + 1 )

Answered by Thiyagarajan K | 06 Aug, 2019, 06:57: AM
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