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Introduction to Points, Vectors, And Functions - At A Glance:

We've been through apples, oranges and mythological creatures unlike anyone has ever seen. But we still don't have a quick way to compare the magnitude of a vector before and after we scale it.

To do this, we have to resort back to one of the oldest tricks in the great book of mathematics: the number 1.

What's the vector equivalent of the number 1? It's a unit vector, which is a vector that has magnitude equal to 1.

Turns out that we can scale any vector to get a unit vector pointing in the same direction. If the vector
has magnitude less than 1, we stretch it.

If the vector has magnitude greater than 1, we shrink it.

The process of scaling a vector to get a unit vector pointing in the same direction is called normalization.

Example 1

Normalize the vector <3,4>.


Example 2

Normalize the vector


Exercise 1

Exercises. Normalize each vector. 

  • <-12,-5>

Exercise 2

Exercises. Normalize each vector. 

  • <1,3>

Exercise 3

Exercises. Normalize each vector. 

  • < 1/2, √3/2 >

Exercise 4

Exercises. Normalize each vector. 

  • < -√3/2, √3/2>
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