Copy of Vector A has a magnitude of 5 and is at an angle of 29.3 degrees measure

Question

Copy of Vector A has a magnitude of 5 and is at an angle of 29.3 degrees measured counter-clockwise from the x axis. Vector B has a magnitude of 12 and is at an angle of 105.4 degrees measured counter-clockwise from the x axis. Vector C has a magnitude of 17 and is at an angle of 180 degrees measured counter-clockwise from the x axis. Lastly, Vector D has a magnitude of 16 and is at an angle of 283 degrees measured counter-clockwise from the x axis. If R = A + B + C - D, find the magnitude of R.

Explanation / Answer

Here ,

for the vectors

A = 5 * (cos(29.3) i + j * sin(29.3))

A = 4.36 i + 1.96 j

B = 12 * cos(105.4) i + j * 12 * sin(105.4)

C = - 17 * i

D = 16 *(cos(283) i + j * sin(283))

Now , R = A + B + C + D

R = 4.36 i + 1.96 j + 12 * cos(105.4) i + j * 12 * sin(105.4) - 17 i - 16 *(cos(283) i + j * sin(283))

R = -19.4 i + 29.11 j

magnitude of R = sqrt(19.4^2 + 29.11^2)

magnitude of R = 35 m

the magnitude of R is 35 m

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