physics
posted by george .
For 3 vectors, find the magnitude and direction of the vector D=AB+3C.
A of length 6.2 and pointing 52 degrees up from the negative xaxis
B of length 6.6 and pointing 27 degrees up from the positive xaxis
C of length 2.8 and pointing 57 degrees down from the positive xaxis
the direction is counterclockwise from the xaxis

First, find the x and y components of all vectors:
Ax = 6.2*cos(52)
Ay = 6.2*sin(52)
Bx = 6.6*cos(27)
By = 6.6*sin(27)
Cx = 2.8*cos(57)
Cy = 2.8*sin(57)
Dx = Ax  Bx + 3*Cx
Dy = Ay  By + 3*Cy
D has a magnitude of
D = (Dx^2 + Dy^2)^0.5
and a direction of theta given by
tan(theta) = Dy/Dx
Input values into these equations and solve