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Lecture 8

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

Course Code
MATH 240
Raluca Rosca

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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.
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
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