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Unit Vector and Components of a Vector

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Unit Vectors in Physics
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Unit Vector

A unit vector is a vector with a magnitude of one unit.

Any vector has an associated unit vector in the same direction but having a magnitude of one. Any vector can be expressed as a scalar multiple of its unit vector.

The following diagram shows how to normalize a vector or how to determine a unit vector. Scroll down the page for more examples and solutions of how to find a unit vector.
Unit Vector

Finding the Unit Vector given a vector (divide the vector by its magnitude).

Finding the vector u given the initial point and the terminal point, then finding the length of the vector and finally finding the unit vector.

Unit vectors have a magnitude of one, and the specific unit vectors i and j represent the positive horizontal and vertical unit vectors in a two dimensional plane. We can write any two dimensional vector in terms of these two unit vectors, and that notation is often seen in Calculus.
How to express a vector algebraically in terms of the unit vectors i and j. This video explains how to determine a unit vector given a vector. It also explains how to determine the component form of a vector in standard position that intersects the unit circle. Expressing a vector as the scaled sum of unit vectors. Unit Vector Notation (part 2).
Showing that adding the i and j components of two vectors is equivalent to adding the vectors visually using the head-to-tail method. Next set of videos in this series

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