Find the coordinates of $\vec{v}$ if $\vec{v}=2\vec{a}-3\vec{b}+4\vec{c}$ and $\vec{a}(4;1),\vec{b}(1;2)$ and $\vec{c}(2;7)$. Find the coordinates of $\vec{v}$ if $\vec{v}=2\vec{a}-3\vec{b}+4\vec{c}$ and $\vec{a}(4;1),\vec{b}(1;2)$ and $\vec{c}(2;7)$.
I am not very familiar with the notation and the way I am supposed to write down such problems. For example, the vector $2\vec{a}$ has coordinates $(8;2)$. Can I write this as $2\vec{a}(8;2)$? Secondly, should I consider the vector $-3\vec{b}$ or $3\vec{b}$? So $-3\vec{b}(-3;-6)$ or $3\vec{b}(3;6)$. Finally, the vector $4\vec{c}$ has coordinates $(8;28).$ Can I write this as $$\vec{v}=2\vec{a}(8;2)-3\vec{b}(...)+4\vec{c}(8;28)$$

From what I understand, $\vec{u}(p;q)$ means that $\vec u$ is a vector in $\Bbb R^2$, with coordinates $(p,q)$.
So, $$\vec v = 2\vec a - 3\vec b + 4\vec c = 2(4,1) - 3(1,2) + 4(2,7) = (13, 24)$$
In your notation, $\vec v(13;24)$.
