Question

Given the points A(-3,0), B(7,17), C(1,4), D(6,4), E(V6,vo), and F(6/6,-4/6) , find the position vector equal to the following vectors AB

Answer 1

The position vector equal to the vector AB is
`\(\overrightarrow{AB} = \begin{bmatrix} 10 \\ 17 \end{bmatrix}\)`.

Step-by-step explanation:

To find the position vector equal to the vector AB, we utilize the coordinates of points A(-3,0) and B(7,17). The position vector of AB is derived by subtracting the coordinates of point A from the coordinates of point B, as position vectors represent the direction and magnitude between two points.

The position vector
`\(\overrightarrow{AB}\)` is calculated as follows:
`\(\overrightarrow{AB} = \begin{bmatrix} x_B - x_A \\ y_B - y_A \end{bmatrix}\)`. Substituting the coordinates of points A(-3,0) and B(7,17) into this formula gives us
`\(\overrightarrow{AB} = \begin{bmatrix} 7 - (-3) \\ 17 - 0 \end{bmatrix} = \begin{bmatrix} 10 \\ 17 \end{bmatrix}\).`

Hence, the position vector representing the vector AB in the coordinate system is
`\(\overrightarrow{AB} = \begin{bmatrix} 10 \\ 17 \end{bmatrix}\)`. This vector demonstrates the displacement and direction from point A to point B, encapsulating both magnitude and direction in terms of x and y components.