# Lecture 1: Dot product

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Lesson Summary:

In this lesson, you will learn about dot products of three-dimensional vectors. A vector is a quantity that has both a direction and a magnitude, and can be represented in terms of its components along the coordinate axis. Vector addition and multiplication by a scalar are also covered. Dot product is a way of multiplying two vectors to get a scalar, and its geometric definition leads to the length of A times the length of B times the cosine of the angle between them. The law of cosines is used to understand the relation between dot product and length of two different vectors.

Lesson Description:

Learn about dot products of three dimensional vectors.

Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 14, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.

• What is a dot product?
• What is a vector?
• How are vectors used in Calculus 3?
• How do you find the length of a three dimensional vector?
• How do you add or subtract vectors?
• How do you multiply a vector by a scalar?
• How do you find the dot product of two vectors?
• What is the formula for the dot product of two vectors?
• What does the dot product of vectors mean geometrically?
• What are some applications of computing a dot product?
• How can you find the angle between two vectors?
• How do you know when the sign of the dot product of two vectors will be positive, negative, or 0?
• How can you tell if two vectors are orthogonal?
• What does it mean when the dot product of two vectors is 0?
• #### Staff Review

• Currently 4.0/5 Stars.
This video explains in depth what vectors are, what taking the dot product means, and why it is useful. This is a very important lecture in Multivariable Calculus. Make sure to watch and understand this lecture on vectors and the dot product if you want to understand this course.