This

**preview**shows half of the first page. to view the full**2 pages of the document.**Math240 Lecture 8: Unit Vectors, Dot Product

Recall that a unit vector is any vector with a magnitude of 1. But did you know we can make any

old vector into a unit vector? Yes, we can!

Given a nonzero vector , then vector will be a unit vector if u=

Here’s what I mean.

Example

1. Find a unit vector that points in the same direction of .

All we do is take the magnitude of .

So the unit vector is then

So that is the unit vector. But how do we check if it is indeed the unit vector?

Easy, we take the magnitude and see if it is equal to 1.

So indeed, u is the unit vector.

2. Find the unit vector going in the opposite direction.

For this, all we do is pop a negative sign on the front of the vector.

The Dot Product

Given two vectors and the angle between them, we can calculate the dot product of two

vectors.

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