The magnitude of two vectors are equal and angle between them is theta. Show that their resultant divides angle theta equally. 

Asked by Moorti | 18th Apr, 2019, 04:43: PM

Expert Answer:

l e t space u s space a s u u m e space t h e space m a g i n t u d e space o f space v e c t o r space i s space A space a n d space t h e space a n g k e space b e t w e e n space t h e space v e c t o r s space i s space theta space a n d space ϕ space i s space t h e space a n g l e space m a d e space b y space r e s u l tan t space w i t h space o n e space o f space t h e space v e c t o r
s o space f r o m space p r a l l e log r a m space l a w space o f space v e c t o r space a d d i t i o n space w e space c a n space w r i t e
tan ϕ space equals fraction numerator b sin theta over denominator a plus b cos theta end fraction space space left parenthesis space h e r e space a space a n d space b space i s space m a g n i t u d e space o f space t w o space v e c t o r s space a n d space theta space i s space t h e space a n g l e space b e t w e e n space t h e m right parenthesis
g i v e n space a equals b equals A
tan ϕ space equals fraction numerator A sin theta over denominator A plus A cos theta end fraction space equals space fraction numerator S i n theta over denominator 1 plus cos theta end fraction
a g a i n space sin theta space equals space space 2 sin theta over 2 cos theta over 2
a n d space 1 plus cos theta space equals space space 2 cos squared theta over 2
p u t t i n g space t h e s e space v a l u e s space w e space g e t space
tan ϕ space equals space fraction numerator 2 sin begin display style theta over 2 end style cos begin display style theta over 2 end style over denominator 2 cos squared begin display style theta over 2 end style end fraction
t a n ϕ space equals space fraction numerator sin begin display style theta over 2 end style over denominator cos begin display style theta over 2 end style end fraction
t a n ϕ space equals space tan theta over 2
t h e s e space v a l u e space o f space t a n space c a n space o n l y space b e space e q u a l space w h e n space space ϕ equals theta over 2
H e n c e space p r o o v e d

Answered by Ankit K | 18th Apr, 2019, 11:06: PM