Unit Vectors i and j | Dot Product | Angle Between Vectors | Orthogonal Vectors

In this lesson, we will learn how to find a unit vector (vector with a magnitude of 1) in the direction of some vector v. Additionally, we will learn how to find the dot product of two vectors (u dot v). Lastly, we will learn how to find the angle between two vectors and determine if vectors are orthogonal vectors.

0:00 Introduction
0:10 Finding a unit vector u in the direction of the vector v
6:10 Finding a unit vector u in the opposite direction of the vector v
9:02 Writing a linear combination of the unit vectors i and j
13:31 Dot product
14:32 Dot product example #1
15:38 Dot product example #2
16:23 Angle between two vectors formula
17:20 Angle between two vectors example #1
20:44 Angle between two vectors example #2
22:59 Orthogonal Vectors
24:04 Are the two vectors orthogonal example #1
26:06 Determine b such that the two vectors are orthogonal example #1