Magnitude and direction of a resultant vector.
Problem: Find the magnitude and direction of the resultant of two vectors and with magnitudes of 6 and 8 and an angle of 60° between them.
Okay, so the first thing I do is find θ by subtracting 60° from 180° and yield 120°. Then I use cosine law to find the magnitude:
Alright, so I got the magnitude right according to my book, and then I go on to draw the vectors, tail-to-tail and then the resultant: Vector diagram
So, now I use sine law to find angle alpha:
° is the direction I get after using sine law, but the answer is completely different in my textbook. The reason why is because they drew first then tail to tail, but I did not learn any law in which there is a general convention to draw vectors of differing magnitudes from tail to tail, therefore I dismissed it as arbitrary. If there is no law, then by using sine law, shouldn't I have arrived at the same direction as the book? The answer in the book:
α ≈ 34.7°, "the resultant of and is approximately 34.7° from ."
So, where did I go wrong? Thanks in advance.