#### Answer

a. B - 3A = (-131.37 units, -40.01 units). Magnitude 137.32, direction 16.93$^o$.
b. 2A - 3B + C = (122.16 units, -86.59 units). Magnitude 150, direction 35.53$^o$.

#### 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 subtracting multiples of the corresponding components.
B - 3A = (-131.37 units, -40.01 units)
Both components are negative, so the vector is in the 3rd quadrant.
b. Again, take the difference by adding and subtracting multiples of the corresponding components.
2A - 3B + C = (122.16 units, -86.59 units)