Find the resultant vectors if the given changes are made in the indicated examples of this section.

In Example 4, find the resultant if 70° is changed to 20°.

Data from Example 4

Find the resultant of the three given vectors in Fig. 9.25. The magnitudes of these vectors are T = 422, U = 405, and V = 210.

We will start by changing each given angle to a standard-position angle (abbreviated SP Angle). In the following table, we show the x- and y-components of the given vectors, and the sums of these components give us the components of R.

We now use the components of R to find its magnitude and reference angle:

Because R_x is positive and R_y is negative, we know that θ is a fourth-quadrant angle. Therefore, to find θ, we subtract θ_ref from 360°. This means θ = 360° − 48.8° = 311.2°

70.0 U 35 0 (a) X U 0 U Fig. 9.25 (b) Tx X 0 Ry R R X