When we multiply a vector by an scalar, it's the same as multiply all the coordinates by the same scalar, so let's suppose I have a vector "u" and multiply by the scalar "λ"
[tex]\Large\displaystyle\text{$\begin{gathered}u = \left(x, y\right)\\ \\\lambda u = \left(\lambda x, \lambda y\right)\end{gathered}$}[/tex]
Just multiply everything by "λ"!
So we have
[tex]\Large\displaystyle\text{$\begin{gathered}\frac{35}{2}\left(\frac{6}{5}v\right)\end{gathered}$}[/tex]
We can simplify the fraction
[tex]\Large\displaystyle\text{$\begin{gathered}\frac{35}{2}\cdot \frac{6}{5}v\\ \\7\cdot 3 v\\ \\21 v\end{gathered}$}[/tex]
So we want to multiply v by the scalar 21, it means that we'll multiply all coordinates by 21, we know that v = (5, 6).
[tex]\Large\displaystyle\text{$\begin{gathered}21v = 21\left(5,6\right)\\ \\21v = \left(21\cdot 5,21\cdot 6\right)\\ \\21v = \left(21\cdot 5,21\cdot 6\right)\\ \\21v = \left(105,126)\\ \\\end{gathered}$}[/tex]
So
[tex]\Large\displaystyle\text{$\begin{gathered}21v = \left(105,126)\\ \\\end{gathered}$}[/tex]
Hope you liked it
Question? Ask me in the comments
