Unit Vectors I and J - Dot Product - Angle Between Vectors - Orthogonal Vectors

Overview

Explore key concepts in vector mathematics in this 28-minute video lesson from GreeneMath.com. Learn how to find unit vectors in the direction of a given vector, calculate dot products, determine angles between vectors, and identify orthogonal vectors. Follow along with step-by-step examples covering topics such as linear combinations of unit vectors i and j, dot product calculations, and the formula for finding angles between vectors. Gain practical skills in solving problems related to unit vectors, dot products, and orthogonality, enhancing your understanding of vector operations and their applications in mathematics and physics.

Syllabus

Introduction.
Finding a unit vector u in the direction of the vector v.
Finding a unit vector u in the opposite direction of the vector v.
Writing a linear combination of the unit vectors i and j.
Dot product.
Dot product example #1.
Dot product example #2.
Angle between two vectors formula.
Angle between two vectors example #1.
Angle between two vectors example #2.
Orthogonal Vectors.
Are the two vectors orthogonal example #1.
Determine b such that the two vectors are orthogonal example #1.