# Position Vectors

# Position Vectors

**Definition**

- A
**position vector**describes the position of a point in space relative to an origin. - It is a vector that starts from a fixed point, usually the origin (0,0) in 2D or (0,0,0) in 3D, and ends at the point under consideration.

**Notation and Description**

- The position vector of a point A is often denoted by
**OA**. - It is represented by the coordinates of the point A with respect to the origin.
- In two-dimensions, a position vector would be ai + bj; whereas, in three dimension, it would be ai + bj + ck.

**Operations**

- Position vectors can be
**added**,**subtracted**, and**multiplied by scalars**, just like any other vectors. - When subtracting two position vectors, the order matters: the vector
**BA**points from A to B, while**AB**points from B to A.

**Distance between Two Points**

- The
**distance between two points**A and B, can be found using their position vectors. The vector**AB**can be found by subtracting**OA**and**OB**(i.e.,**AB = OB - OA**) and the distance can be found by calculating the magnitude of**AB**.

**Importance**

- Position vectors are fundamental in vector algebra and physics as they allow for a concrete understanding of points in space.
- They pave the way for describing geometrical transformations, such as rotation, translation, and scaling.

**Applications**

**Analytical geometry**makes extensive use of position vectors to define geometric objects such as lines and planes.- In
**Physics**, position vectors are crucial for understanding concepts such as displacement, velocity, and acceleration. - In
**computer graphics**, they play a key role in representing objects in a 3D space.