Final answer:
To find the magnitude and direction of the resultant vector R, we can use graphical methods. First, find the components of vectors A and B along the x and y axes. Then, use the Pythagorean theorem to find the magnitude of R and the inverse tangent function to find the direction of R.
Step-by-step explanation:
To find the magnitude and direction of the resultant Vector B, with a magnitude of 4 units, points along the negative y-axis, so its x-component is 0 and its y-component is -4.
To find the components of R, we can simply add the corresponding components of A and B: Rx = Ax + Bx
= 3 + 0 = 3, Ry = Ay + By = 0 + (-4) = -4.
Using the Pythagorean theorem, we can find the magnitude of R: R = sqrt(Rx^2 + Ry^2)
= sqrt(3^2 + (-4)^2) = sqrt(9 + 16) = sqrt(25) = 5 units.
To find the direction of R, we can use the inverse tangent function: Rtheta = atan(Ry/Rx)
= atan((-4)/3)
= atan(-4/3) = -53.13 degrees.
However, since vector B points along the negative y-axis, the direction of R is 90 degrees minus the calculated angle: Rtheta = 90 - 53.13 = 36.87 degrees.
Therefore, the magnitude of R is 5 units and it points at an angle of 36.87 degrees north of the x-axis.