Step-by-step explanation:
For any two vectors [tex]v_{1}[/tex] and v[tex]_{2}[/tex] to be equivalent,
their length and direction has the same.
Distance between two points [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex]
is [tex]\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^{2}}[/tex]
Length of [tex]v_{1}[/tex] is [tex]\sqrt{(6-3)^{2}+(6-2)^{2}}=\sqrt{9+16}=\sqrt{25}=5[/tex]
Length of [tex]v_{2}[/tex] is [tex]\sqrt{(6-2)^{2}+(6-3)^{2}}=\sqrt{16+9}=\sqrt{25}=5[/tex]
Slope of vector [tex]v[/tex] joining [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] is [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
slope of [tex]v_{1}[/tex] = [tex]\frac{6-3}{6-2} =\frac{3}{4}[/tex]
slope of [tex]v_{2}[/tex] = [tex]\frac{6-2}{6-3} =\frac{4}{3}[/tex]
since slope of [tex]v_{1}[/tex] is not equal to slope of [tex]v_{2}[/tex],the vectors are not equivalent.
