Initial point

Definition

The initial point of a vector is the starting point from which the vector originates. It is often denoted as the coordinate $(x_1, y_1)$ in a two-dimensional plane or $(x_1, y_1, z_1)$ in three-dimensional space.

5 Must Know Facts For Your Next Test

1. The initial point is crucial for determining the direction and magnitude of a vector.
2. In vector notation, it is typically paired with a terminal point to define the entire vector.
3. When given two points, you can find the vector by subtracting the coordinates of the initial point from those of the terminal point.
4. The standard position of a vector has its initial point at the origin $(0,0)$ or $(0,0,0)$.
5. In physics and engineering, knowing the initial point helps in calculating displacement and other vector-related quantities.

Review Questions

• How do you determine a vector given its initial and terminal points?
• What is the significance of placing a vector in standard position?
• How does changing the initial point affect the direction and magnitude of a vector?

Related terms

Terminal Point: The endpoint of a vector indicating where it ends.

Magnitude: A measure of how long a vector is; calculated using distance formula between initial and terminal points.

Standard Position: A convention where vectors have their initial points at the origin.