LESSON 1: Unit Vectors


To find a unit vector of a vector, you first find the magnitude of the vector. Then, divide each component of the vector by its magnitude. Here is an example continued from the last section:





As you can see from the example, each component of the unit vector is less than 1. This is true for all unit vectors. If you take the magnitude of this unit vector you should find that its magnitude is 1. This is also true for all unit vectors. Remember these two rules for unit vectors: Rule 1: Each component of a unit vector is less than 1. Rule 2: All unit vectors have a magnitude of 1.

The main purpose of a unit vector is to display direction. Notice that the x-component of this unit vector is -.487, the y-component is -.811, and the z-component is .324. The negative signs simply indicate direction. The negative sign for the x-component, for example, indicates that rather than pointing to the right, this vector points to the left (assuming that the graph indicates a positive x-axis to the right).

It may help you gain a better understanding of unit vectors to think of the components as percentages. For instance, this vector
points 48.7 percent in the x-direction, 81.1 percent in the y-direction, and 32.4 percent in the z-direction. Although this is inaccurate (48.7 + 81.1 + 32.4 does not equal 100) , the idea is correct; this vector points mostly in the y-direction, a bit less in the x-direction, and least in the z-direction.

The next section is the last section of lesson one, in this section we will expand our knowledge of unit vectors by relating them to cos angles. Lesson 1: Cos Angles.