1. 3. (a) The forces are balanced when they sum to zero: F1 + F2 + F3 = 0. This means
F3 = −F1 − F2 = −(10 N) ˆ + (4 N) ˆ − (17 N) ˆ − (2 N) ˆ = (−27 N) ˆ + (2 N) ˆ .
i j i j i j
(b) If θ is the angle the vector makes with the x axis then
F3y 2N
tan θ = = = −0.741 .
F3x −27 N
The angle is either −4.2◦ or 176◦ . The second solution yields a negative x component and a positive
y component and is therefore the correct solution.