Question

Given f = <4, -3> and g = <-2, 1>, what is f - 2g ?<2, -2><8, -5><6, -4><0, -1>

Answer 1

Recall the following rules for operating with vectors:

`\begin{gathered} \langle x_A,y_A\rangle+\langle x_B,y_B\rangle=\langle x_A+x_B,y_A+y_B\rangle \\ k\langle x_A,y_A\rangle=\langle kx_A,ky_A\rangle \end{gathered}`

Use the second rule to find -2g:

`\begin{gathered} g=\langle-2,1\rangle \\ \Rightarrow-2g=-2\langle-2,1\rangle \\ =\langle-2(-2),1(-2)\rangle \\ =\langle4,-2\rangle \end{gathered}`

Find f-2g as f+(-2g) using the first rule:

`\begin{gathered} f=\langle4,-3\rangle \\ \\ \Rightarrow f-2g=\langle4,-3\rangle-2\langle-2,1\rangle \\ =\langle4,-3\rangle+\langle4,-2\rangle \\ =\langle4,-3\rangle+\langle4,-2\rangle \\ =\langle4+4,-3-2\rangle \\ =\langle8,-5\rangle \end{gathered}`

Therefore, the correct choice is:

`\langle8,-5\rangle`