Given:
[tex]\begin{gathered} A_x=\text{ 7.6} \\ A_y\text{ = -9.2} \\ B_x=-3.8 \\ B_y=\text{ 4.6} \end{gathered}[/tex]
To find the equation that describes the relationship.
Explanation:
The vector A will be
[tex]\begin{gathered} A=A_x+A_y \\ =\text{ \lparen7.6\rparen}_x\text{ +\lparen-9.2\rparen}_y \end{gathered}[/tex]
The vector B will be
[tex]\begin{gathered} B=\text{ B}_x+B_y \\ =(-3.8)_x+(4.6)_y \end{gathered}[/tex]
The vector B can be written as
[tex]\begin{gathered} B=\text{ -\lbrack\lparen3.8\rparen}_x-(4.6)_y\text{\rbrack} \\ \frac{1}{2}\text{ B}=\text{ -}\frac{1}{2}[\text{\lparen3.8\rparen}_x-(4.6)_y] \\ B=-\frac{1}{2}[2\times\lbrace\text{\lparen3.8\rparen}_x-(4.6)_y\rbrace] \\ =-0.5[(7.6)_x-(9.2)_y] \\ B=-0.5\text{ A} \end{gathered}[/tex]
