Question

Find the vectors u and v whose initial and terminal points are given
,

Answer 1

To find the vectors \( \mathbf{u} \) and \( \mathbf{v} \) based on given points, we need the coordinates of these points. The general formula for a vector represented by its initial point \( (x_1, y_1) \) and terminal point \( (x_2, y_2) \) in 2D is:

\[
\mathbf{u} = (x_2 - x_1, y_2 - y_1)
\]

For example, if \( \mathbf{u} \) has initial point \( A(x_1, y_1) \) and terminal point \( B(x_2, y_2) \), the vector \( \mathbf{u} \) can be calculated as follows:

- Initial point \( A \): \( (x_1, y_1) \)
- Terminal point \( B \): \( (x_2, y_2) \)

Then,

\[
\mathbf{u} = (x_2 - x_1, y_2 - y_1)
\]

Similarly, if you have another vector \( \mathbf{v} \) with its own initial and terminal points, say \( C(x_3, y_3) \) and \( D(x_4, y_4) \):

\[
\mathbf{v} = (x_4 - x_3, y_4 - y_3)
\]

Please provide the coordinates of the specific points for \( \mathbf{u} \) and \( \mathbf{v} \), and I can compute the vectors for you.