Two forces P and Q act on a particle. The force P has magnitude 7 N and acts due north. The resultant of P and Q is a force of magnitude 10 N acting in a direction with bearing 120°. Find the magnitude of Q and the bearing of Q.

There are 2 methods to solving this- the visual method and the kinesthetic method. Here I will use the visual one. We start by creating a vector triangle. We are going to use R = P + Q, where R is the resultant force of P and Q, to find the magnitude and bearing of Q. We know that P = 0i + 7j so now we find R by creating a right angle triangle. Using SOHCAHTOA, we get Sin30 = O/10 and Cos30 = A/10 which gives us O = 5 and A = 5Root[3]. So now we have R = 5Root[3]i - 5j. We can not insert these vectors into Q = R - P to get Q = 5Root[3]i - 5j - 0i - 7j = 5Root[3]i - 12j. Using Pythagoras' theorem, we find the magnitude of Q = Root[(5Root[3])^2 + 12^2] = 14.8N to 3dp. Next we find theta using SOHCAHTOA with the formula theta = Tan^-1(12/5Root[3]) to get theta = 54.18247436. We then add 90 and round to 3sf to get a bearing of 144 degrees.