# How to add vectors and calculate the resultant angle?

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.

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.
• $C = {3 \choose 1}$ and $J = {-4 \choose -3}$ right? Then you are adding up the $x$-components and $y$-components separately: $3+(-4)=-1$, $1+(-3) = (-2)$. Sep 6, 2019 at 13:45