25. Find the length of the vector: a) $\vec{a}=(5 ; 12) ;$ b) $\vec{b}=(7 ;-1)$.
Solution. According to formula (1), we have:

a) $|\vec{a}|=\sqrt{x^{2}+y^{2}}=\sqrt{25+144}=\sqrt{169}=13$;
b) $|\vec{b}|=\sqrt{x^{2}+y^{2}}=\sqrt{49+1}=\sqrt{50}=5 \sqrt{2}$.