Question

Given u=<2,1> and v=<5,3> find 2u-3v

Answer 1

To answer this question we will use the following properties of vectors:

`\begin{gathered} a=, \\ +=. \end{gathered}`

Substituting u=<2,1> and v=<5,3> in the given expression we get:

`2<2,1>-3<5,3>.`

Applying the first property we get:

`\begin{gathered} \lt2*2,2*1\gt+\lt(-3)*5,(-3)3\gt, \\ <4,2>+<-15,-9>. \end{gathered}`

Applying the second property to the above result we get:

`\begin{gathered} <4-15,2-9>, \\ <-11,-7>. \end{gathered}`

Answer:

`<-11,-7>.`