<s>[INST] Angle between two lines explanation I gave two lines $q_1 = 2x - y + 2 = 0$ and $q_2 = x + 2y - 3 = 0$. 
They have vectors $n_1 = (2,1)$ and $n_2 = (1,2)$. 
When I have to find angle between them I must apply that formula: 
$$\cos \theta = \frac{2\cdot 1 + (-1)\cdot2}{\sqrt{4 + 1}\sqrt{1 + 4}} = 0 \Rightarrow \theta =  90^\circ$$
Replacing $n_1$ and $n_2$ is clear to me, but can you please explain how I get $90^\circ$ from solving the formula. Thank you.
Where those $\sqrt{4 + 1}\sqrt{1 + 4}$ comes from?
If $ \theta $ is $90^ \circ$ at $0$, how much degrees it will be if it is $\dfrac{1}{5}$?
 [/INST] Let $\theta$ be an angle.
$\cos \theta = \frac{2.1 + (-1).2}{\sqrt 5. \sqrt 5}$
$\cos \theta = \frac{2 - 2}{\sqrt 5. \sqrt 5}$
$\cos \theta = \frac{0}{5}$
$\cos \theta = 0$
$\cos \theta = \cos 90°$
$\theta = 90°$
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