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Lecture 8

MATH 240 Lecture Notes - Lecture 8: Dot Product, Unit Vector, Cross Product

Department
Mathematics
Course Code
MATH 240
Professor
Raluca Rosca
Lecture
8

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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