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
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
Answers
Jennifer
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
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