Question

if vector v has an initial point at (2,3) and a terminal point at (6,6) and vector w has an initial point at (3,2) and a terminal point at (6,6), are the two vectors equivalent?​

Answer 1

Not equivalent

Step-by-step explanation:

For any two vectors $v_{1}$ and v$_{2}$ to be equivalent,

their length and direction has the same.

Distance between two points $(x_{1},y_{1})$ and $(x_{2},y_{2})$

is $\sqrt{(y_{2}-y_{1})^2+(x_{2}-x_{1})^{2}}$

Length of $v_{1}$ is $\sqrt{(6-3)^{2}+(6-2)^{2}}=\sqrt{9+16}=\sqrt{25}=5$

Length of $v_{2}$ is $\sqrt{(6-2)^{2}+(6-3)^{2}}=\sqrt{16+9}=\sqrt{25}=5$

Slope of vector $v$ joining $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

slope of $v_{1}$ = $\frac{6-3}{6-2} =\frac{3}{4}$

slope of $v_{2}$ = $\frac{6-2}{6-3} =\frac{4}{3}$

since slope of $v_{1}$ is not equal to slope of $v_{2}$,the vectors are not equivalent.