We can find the resultant by summing the vector components.....
For the vector pointing "south," the x component is 0 and the y component = 3sin(270) = 3*(-1) = -3
For the one with the magnitude of 7 at 150 degrees, we have
7cos150 = 7*-sqrt(3)/2 = - (7/2)sqrt (3) as the x component and
7sin150 = 7*(1/2) = 7/2 as the y component
The sum of the x components = -(7/2)sqrt(3)
And the sum of the y components = -3 + 7/2 = 1/2
The resulting magnitude is given by :
sqrt [ (-7sqrt(3)/2)^2 + (1/2)^2 ) = sqrt(37) = about 6.083
And the direction is given by:
arctan [ (1/2) / (-(7sqrt(3)/2)] = about -4.715° + 180 = about 175.28° ........this has to be so because the sum of the x components are negative and the sum of the y components are positive.....thus....this must be a 2nd quadrant angle
So......the resultant vector = 6.083<175.28° = (C) seems to come closest to this
