Question

Vector u has its initial point at (15, 22) and its terminal point at (5, -4). Vector v points in a direction opposite that of u, and its magnitude is twice the magnitude of u. What is the component form of v?

Answer 1

`vecv = 20hati+54hatj`

Explanation:

We are given that `vecu` is the vector from `(15,22)` to `(5,-4)`:

`vecu = (5-15)hati+ (-4-22)hatj`

Simplify:

`vecu = -10hati-26hatj`

We are told that `vecv` is in the opposite direction of `vecu`, therefore, `vecv` is `vecu` multiplied by a negative number and it is twice the magnitude so the number is -2:

`vecv = -2vecu`

`vecv = -2(-10hati-26hatj)`

`vecv = 20hati+54hatj`