Three vectors a, b, and c each have a magnitude of 70 m and lie in an xy plane.

Question

Three vectors a, b, and c each have a magnitude of 70 m and lie in an xy plane. Their directions relative to the positive direction of the x axis are 25 degree, 210 degree, and 310 degree, respectively. (Take these angles counterclockwise to the positive direction of the x axis) What is the magnitude of the vector a + b + c? What is the angle of the vector a - b + c? What is the magnitude of a - b + c? What is the angle of a - b + c? What is the magnitude of a fourth vector d such that (a + b) - (c + d) = 0? What is the angle of a fourth vector d such that (a + b) - (c + d) = 0?

Explanation / Answer

a = 70(cos(25)i + sin(25)j)
b = 70(cos(210)i + sin(210)j)
c = 70(cos(310)i + sin(310)j)

a) a + b + c = 70(0.683i - 0.843j)
mag = 75.97345
b) tyheta = arctan(-0.843/0.683) = -50.98 deg
d) a - b + c = 70(2.4151i + 0.156j)
theta = arctan(0.156/2.4151) = 3.709 dseg
e) d = -70(0.683i - 0.843j)
|d| = 75.97345
f) Angle = 129.02 deg

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