# Lecture 2: Determinants & cross product

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Lesson Summary:

In this lecture, you will learn about important concepts in vector operations such as finding determinants and cross products, and their various applications. You will see how dot products can be used to find lengths, angles, and components of vectors along a given direction. You will also learn about the determinants of vectors and how they can be used to find the area of triangles and parallelograms in the plane, as well as the volume of solids in space. Finally, you will be introduced to cross products and their applications in finding the area of surfaces and determining orientation in space.

Lesson Description:

Learn about finding determinants and cross products of vectors and their applications.

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.

• How do you find a determinant of two vectors?
• How do you find the cross product of two vectors?
• What is a cross product?
• What are some applications of finding a dot product?
• What is a unit vector?
• How do you find a unit vector?
• How do you find the projection of a vector in a direction?
• How do you find the components of a vector along a unit vector?
• How do you find the area of a polygon using vectors?
• How do you find the area of a triangle using vectors?
• What is the vector formula for the area of a triangle?
• How do you find the area of a parallelogram using vectors?
• What does the cross product of two vectors mean geometrically?
• How do you know if the direction of a cross product is up or down?
• What is the right-hand rule?
• How can you find the direction of the cross product of two vectors?
• How do you find the volume of a box using vectors?
• How do you find the determinant of three vectors?
• What is the handedness of coordinates?
• How do you find the length of a cross product of two vectors?
• #### Staff Review

• Currently 4.0/5 Stars.
This lesson starts with a quick review of dot products between vectors, and moves on to cross products and determinants. This is another very important lecture in Multivariable Calculus, taught very well and understandably. This is a really great lecture overall.