Three vectors, each have a magnitude of 30 units, have their tails at the same oint and are directed 120 degrees from each other. Make a statement concerning the sum of these three vectors.

Question

a) the sum vector is 0
b) the sum vector is greater thatn 30
c) the sum vector is equal to 30
d) the sum vector is less than 30

c) would be the correct answer right? I did v=sqrt(v_x^2 +v_y^2) and got 29.9993 which is quite close to 30.

Answer 1

Do the math in polar:

a@0 + a@120 + a@240

Well, the y components of all three of those add to zero.

Now, the x components is a+ -2a*cos60
which is...

Answer 2

Fr = 30[0o] + 30[120o] + 30[240o].
Fr = 30 + (-15+26i) + (-15-26i),
Fr = 0 + 0i = 0. = Resultant force.

Therefore, the vectors are in equilibrium.