CHAPTER 02.09: VECTORS: What is a unit vector? Example

In this segment we will look at some examples of a unit vector. So for example, let’s suppose somebody says “hey can you give me a three dimensional column vector which is a unit vector?” So all I will do is I can say is this one is a unit vector 1 divided by square root of 3, 1 divided by square root of 3, 1 divided by square root of 3. Why is it a unit vector? Because its magnitude is one because if I take the square root of the square of each of the components addition. So the first component is 1 divided by the square root of 3 I square it; the second component is 1 divided by the square root of 3 I square it; the third is 1 divided by the square root of 3 I square it. So I get that and the square root of what is 1 by 3, plus 1 by 3, plus 1 by 3 the square root of 1 and that comes out to be 1. So that is a unit vector.

Another example of a unit vector can be 0, 1, 0, a three dimensional column vector which is a unit vector is like 0, 1, 0. Another one can be 1 divided by square root of 2, 1 divided by square root of 2, and 0. So from the example, in this case I will square each of the components 1 by 2 square root of 2 squared, 1 by square root of 2 squared plus 0 squared so I get square root of 1 by 2 plus 1 by 2 plus 0 I get square root of 1 and I get 1 from there. So that’s also a unit vector; so we can come up with different examples for unit vectors like that. And that’s the end of this segment.