Lecture 3, Friday, 8/29/08: Section 10.4: The cross product

Determinants (2 by 2 and 3 by 3)
The cross product: Algebraic definition (in terms of 3 by 3 determinants) and geometric interpretation
Cross products of parallel vectors
Cross products of standard basis vectors
Properties of the cross product (Th. 4.3, p. 819)
Triple products: Scalar triple product and vector triple product
Finding a vector perpendicular to two given vectors
Computing the area of a parallelogram or a triangle using cross products
Computing the volume of a parallelepiped using the scalar triple product
Testing if three given vectors are coplanar (i.e., lie in the same plane)
Computing the distance of a point to a line. (This will be covered in the next lecture together with another distance formula.)
Determining whether a given expression involving dot and/or cross products represents a vector, scalar, or does not makes sense. (The book does not have problems on this, so I prepared a Problem Set. Most of these problems I discussed in the lecture in connection with triple products.)

Section 10.4. Optional: Examples 4.7 and 4.8.

Section 10.4: 1, 5, 13, 21, 47, 49, 53, 55, 57, 59. Solutions.

Last modified Sun 31 Aug 2008 05:38:37 PM CDT