Vector Diagram I answered this question correctly but am really struggling to find out how I did it?
What I thought I had to do was to count the length and width of the arrows for the letters it asks to add up.
Once I get these 2 values from each letter I use -tan(c/j) However after trying this I caunt seem to get the correct answer again. Would appriciate some help as to where im going wrong or if im on the right track at all.
On
The sum is ${-1 \choose -2}$. The resultant angle is the angle that the vector makes with respect to the $x$-axis. This will be an angle in the range $[0^\circ, 90^\circ]$. All that matters are the lengths of the sides relative to the angle $\theta$. No minus signs! Lengths are non negative. In this case $\tan \theta = \dfrac 21 = 2$. So $\theta = \arctan 2 \approx 63^\circ$
The resultant should be ${3 \choose 1} + {-4 \choose -3} = {-1 \choose -2}$.
What you are doing is not correct. You should use the inverse tangent in this case: since $\tan \theta = \frac{-2}{-1}$ (opposite over adjacent), $\theta = \tan^{-1} \frac{-2}{-1} = 63.4º$.
If you don't like to use negatives, the vector has the same resultant as ${1 \choose 2}$, which also gives the same answer.