Position Vector

Related Topics: More Vector Lessons

In these lessons, we will learn what is a position vector and how to find a position vector for a vector between two points.

What is a Position Vector?
A vector that starts from the origin (O) is called a position vector.

In the following diagram, point A has the position vector a and point B has the position vector b.

Example:

Tutorial on Vectors
What are 2-dimensional Vectors, 3-dimensional Vectors, Displacement Vectors and Position Vectors?
How to find the Position Vector?
Example: P is the point (3, 4). $$\overrightarrow {PQ} = \left( {\begin{array}{*{20}{c}}{ - 6}\\3\end{array}} \right)$$. Find the position vector of Q.

Vectors in R2 and R3
Position Vector and Magnitude / Length.
How to find a position vector for a vector between two points and also find the length of the vector?

Example:
a) Find the position vector v for a vector that starts at Q(3, 7) and ends at P(-4, 2)
b) Find the length of the vector found in part a)
How to find the position vector between two points?
Example: Find the position vector between the point A(3, 2) and the point B(-2, 1)

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.