#### Answer

a. A – B + C = (53.67 units, -32.31 units). Magnitude 62.6, direction -31.0$^o$.
b. A + B - C = (24.03 units, 73.63 units). Magnitude 77.5, direction 71.9$^o$.
c. C - A - B = (-24.03 units, -73.63 units). Magnitude 77.5, direction 251.9$^o$.

#### Work Step by Step

Use equations 3.3a and 3.3b to find the x and y components. Vector B points at 124 degrees and vector C points at 270 degrees from the positive x-axis.
Vector A = (38.85, 20.66)
Vector B = (-14.82, 21.97)
Vector C = (0, -31)
a. Take the difference by adding and subtracting multiples of the corresponding components.
A – B + C = (53.67 units, -32.31 units)
b. Take the difference by adding and subtracting multiples of the corresponding components.
A + B - C = (24.03 units, 73.63 units)
c. Take the difference by adding and subtracting multiples of the corresponding components.
C - A - B = (-24.03 units, -73.63 units)
Note that the answer to part C is the opposite of the answer to part B.