Question

For 3 vectors, find the magnitude and direction of the vector D=A-B+3C.

A of length 6.2 and pointing 52 degrees up from the negative x-axis

B of length 6.6 and pointing 27 degrees up from the positive x-axis

C of length 2.8 and pointing 57 degrees down from the positive x-axis

the direction is counterclockwise from the x-axis

Answer 1

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