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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 ;-  begin mathsize 12px style cos theta space equals space fraction numerator bold italic A times bold italic B over denominator open vertical bar bold italic A close vertical bar space open vertical bar bold italic B close vertical bar end fraction space equals space fraction numerator a space b over denominator a space cross times space square root of b squared plus c squared end root end fraction space equals space fraction numerator a space b over denominator m end fraction end style ........................(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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