Lecture 1: Dot product
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.
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.
- Lecture Notes - Lecture Notes from this lesson.
- Transcript of Lesson - The written transcript of the lesson.
- Problem Set - A problem set with some problems from this lecture.
- Vector Operations and Properties - A list of some operations and properties using vectors.
- 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?
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Staff Review
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.
