three vectors are shown in fig. 3-32. their magnitudesare given in arbitrary units. determine the sum of the threevectors. give the resultant in terms of (a) components(b)magnitude and angle with the x-axis.

figure 3-32 details:

vector A: A=44.0, begins @ origin, extends into QI withan angle of 28 degrees

vector B: B=26.5, begins @ origin, extends into QII with anangle of 56 degrees

vector C: C=31, begins @ origin, lies directly on -y axis(270 degrees).

### 1 Answer

For the second vector, is the angle ccw from the +y axis, or cw from the -x axis? I’ll assume the latter. If that’s wrong, switch the sin and cos functions.

R = A+B+C = (44cos28 – 26.5cos56 + 0) i + (44sin28 + 26.5sin6 – 31) j

R = 24 i + 11.6 j ← x and y components (a)

(b) mag R = √(24² + 11.6²) = 26.7

Θ = arctan(11.6/24) = 26º