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

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)}=√(9+16)=√(25)=5`

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

Slope of vector
`v` joining
`(x_(1),y_(1))` and
`(x_(2),y_(2))` is
`(y_(2)-y_(1))/(x_(2)-x_(1))`

slope of
`v_(1)` =
`(6-3)/(6-2) =(3)/(4)`

slope of
`v_(2)` =
`(6-2)/(6-3) =(4)/(3)`

since slope of
`v_(1)` is not equal to slope of
`v_(2)`,the vectors are not equivalent.