Question

URGENT!!! Help pls. U could literally just give me the equations

Answer 1

Explanation:

Terminal points of vector u has been given as (4, 0), (9, 4).

Therefore, vector u can be represented by,

`\vec{u}=\vec{u_2}-\vec{u_1}`

`\vec{u}=(9i+4j)-(4i)`

`\vec{u}=5i+4j`

And the magnitude of the vector u will be,

|| u || =
`√(5^2+4^2)`

=
`√(41)`

Slope of vector passing through
`(x_1,y_1)` and
`(x_2,y_2)` is defined by the expression,

Slope =
`(y_2-y_1)/(x_2-x_1)`

Therefore, slope of vector u will be,

Slope =
`(4-0)/(9-4)`

=
`(4)/(5)`

Similarly, terminal points of vector v are (-7, 1) and (3, 9).

So the vector v will be,

`\vec{v}=(3i+9j)-(-7i+1j)`

`\vec{v}=(3i+7i)+(9j-1j)`

`\vec{v}=10i+8j`

Therefore, magnitude of vector v will be,

|| v || =
`√(10^2+8^2)`

=
`√(164)`

=
`2√(41)`

Slope of vector v =
`(9-1)/(3+7)`

=
`(8)/(10)`

=
`(4)/(5)`