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Discussion Response Post to: HC Verma Problems

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ramyani chakrabarty (3105)

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vecor A makes an angle of 20 degree and vector B makes an angle of 110 degree with the X-axis. The magnitudes of these vectors are 3m and 4m respectively

vecor A = i 3 cos 20 + j 3 sin 20
vector B = i 4 cos 110 + j 4 sin 110
Resultant vector = i ( 3 cos 20 + 4 cos 110 ) + j ( 3 sin 20 + 4sin 110)
= i (2..81 --1.36) + j (1.03+3.75)
= i 1.45 + j 4.78
magnitude of Resultant vector = sq.rt ( 1.45² +4.78²) = 4.99 = 5 m ( appx)
If this vector makes an angle thete with X - axis
tan theta = |opp. side| / |base| = 4.78 /1.45 = 3.29
theta = 73 degree

but obviously the better method is to notice the difference of inclination of two vectors which is 110-20= 90. So two vectors r at right angles to each other. Pythagorous is enough.
magnitude of Resultant vector = ^{[2 ]}

(3² + 4² ) = 5 m
tan beta ( angle with vector A ) = 4/ 3 = 53 degree
so the Resultant vector makes angle 53 degree + 20 degree with X axis.

NIT silchar electrical engineering

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