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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

  • physics -

    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

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