Subtraction of vectors.?

Taking the E-W direction as the X-axis and the N-S direction as the Y-axis:

F1 = 500i

F2 = 250j

F2 - F1 = -500i + 250j

Magnitude = sqrt( (-500)^2 + (250)^2) = 250 sqrt(5)

Direction = tan(inv) (250/-500) = tan(inv) (-0,5) with F1

Well, one answer is 250 N due north - 500 N due east, which could be written <250, -500> N in vector notation if that's the way you have your coordinates set up (<y,x>, backwards of the usual way). I'll bet you get 0 credit for that answer, but it's technically correct. Probably what your teacher wants is a pull of 250 N to the north (call that 0 degrees) and a pull of 500 N to the west (that's negative east, so let's call it 270 degrees). Now we have to do trigonometry to find the "resolvent force", which is just the (vector) sum. If you draw a parallelogram (in this case a rectangle) you can find the resulting force (the diagonal) which will be 250 times the square root of 3 (it's a 1,2,sqrt(3) right triangle) (the actual question determines whether you need symbolic answers or numeric) and then the angle of the diagonal. You can give the angle in either terms of 360 degrees or N something W, which is measuring how far west you are from due north. The actual angle is some long decimal number (well, 270 degrees plus arctan(2) (also in degrees). The something in the N something W answer will be 90 degrees minus arctan(2) still in degrees. Be careful about getting arctan(2) in degrees because the default setting on your calculator is probably radians. So your final answer should be something like 433 N N 27 deg W. Note also that your directions are always N deg W and never W deg N, even if it's N 89.95 deg W (almost due west). I don't know why.

Vectors are used to symbolize many stuff that have a value and direction such through fact the stress of gravity on your physique or the cost of a bullet. On a airplane or in area you could characterize a vector via its factors (x,y) or (x,y,z). to characteristic or subtract one vector from yet another, only upload or subract the factors.