Vector A has a magnitude of 71 units and points due west, while vector B has the same magnitude and points due south. Find the magnitude and direction of (a) A + B and (b) A - B . Specify the directions relative to due west.

Answer 1

A = 71[180o]. B = 71[270o].

a. A+B=(71*cos180+71*cos270)+i(71*sin180+71*sin270)
A+B = (-71+0) + i(0-71)
A+B = -71 - i71 = -100.4]45o] or
100.4[45o+180o] = 100.4[225o].
Since the resultant is in Q3, 45o is the
reference angle.

b. A-B=(71*cos180-71*cos270)-i(71sin180-71sin270)
A-B = (-71-0) + i(0-(-71))
A-B = -71 + i71 = -100.4[-45o] or
100.4[-45+180] = 100.4[135o].

Answer 2

A force F1of magnitude 5.00 units acts on an object at the origin in a direction è = 45.0° above the positive x-axis. (See the figure below.) A second force F2of magnitude 5.00 units acts on the object in the direction of the positive y-axis. Find graphically the magnitude and direction of the resultant force F1 + F2.

magnitude

1 units

direction

2° counterclockwise from the +x-axis