Let  magnitude of three vectors a=2; b=3 ; c=6. Angle between any two vector is 120 degree and the vector are coplaner ,find magnitude of resultant vector

Asked by tusharbailwal8 | 22nd Apr, 2019, 07:26: AM

Expert Answer:

l e t space u s space a s s u m e space v e c t o r space a space i s space a l o n g space plus v e space x space a x i s space
t h i s space v e c t o r space c a n space b e space g i v e n space a s space a space equals space 2 i
s o space t h e space v e c t o r space b space w i l l space l i e space i n space 2 n d space q u a d r a n t space w i t h space m a k i n g space a n space a n g l e space o f space 30 space d e g r e e space w i t h space plus v e space y space a x i s
t h i s space v e c t o r space c a n space b e space g i v e n space space a s space b space equals space minus 3 sin 30 space i space plus space 3 cos 30 space j space equals space minus 1.5 space i space plus space 1.5 square root of 3 j
a n d space v e c t o r space c space w i l l space l i e space i n space 3 r d space q u a d r a n space w i t h space m a k i n g space a n space a n g l e space o f space 30 space d e g r e e space w i t h space minus v e space d i r e c t i o n space o f space y space a x i s
t h i s space v e c t o r space c a n space b e space g i v e n space a s space c space equals space minus 6 sin 30 space i minus 6 cos 30 space space equals space minus 3 space i space space minus space 3 square root of 3 space j
n e t space r e s u l tan t space v e c t i r space R space equals space a plus b plus c space equals space 2 i space minus space 1.5 i space plus 1.5 square root of 3 j space minus 3 i minus 3 square root of 3 j
R space equals space minus 2.5 space i space minus 1.5 square root of 3 j
s o space v a l u e space o f space r e s u l tan t space R space equals space square root of left parenthesis 2.5 right parenthesis squared space plus left parenthesis 1.5 square root of 3 right parenthesis squared space end root space equals space square root of 13 space

Answered by Ankit K | 22nd Apr, 2019, 11:48: AM

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