Vector Algebra ? Vector Addition ? Scalar Multiplication ? How about the product of two vectors? 1. Dot Product ?v ? ?u 2. Cross Product ?v ? ?u Before the geometry, Determinant ? Determinant of a 2? 2 matrix, ? ? ? ? a b c d ? ? ? ? = ad ? bc ? Determinant of a 3? 3 matrix, ? ? ? ? ? ? a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 ? ? ? ? ? ? = a 1 ? ? ? ? b 2 b 3 c 2 c 3 ? ? ? ? ? a 2 ? ? ? ? b 1 b 3 c 1 c 3 ? ? ? ? + a 3 ? ? ? ? b 1 b 2 c 1 c 2 ? ? ? ? =a 1 (b 2 c 3 ? b 3 c 2 )? a 2 (b 1 c 3 ? b 3 c 1 ) + a 3 (b 1 c 2 ? b 2 c 1 ) Example 1 1. ? ? ? ? ?1 2 3 5 ? ? ? ? = ?5? 6 = ?11 2. ? ? ? ? ? ? 2 4 6 ?1 3 5 7 2 6 ? ? ? ? ? ? = 2 ? ? ? ? 3 5 2 6 ? ? ? ? ? 4 ? ?

# Cross Product

Vector Algebra ? Vector Addition ? Scalar Multiplication ? How about the product of two vectors? 1. Dot Product ?v ? ?u 2. Cross Product ?v ? ?u Before the geometry, Determinant ? Determinant of a 2? 2 matrix, ? ? ? ? a b c d ? ? ? ? = ad ? bc ? Determinant of a 3? 3 matrix, ? ? ? ? ? ? a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 ? ? ? ? ? ? = a 1 ? ? ? ? b 2 b 3 c 2 c 3 ? ? ? ? ? a 2 ? ? ? ? b 1 b 3 c 1 c 3 ? ? ? ? + a 3 ? ? ? ? b 1 b 2 c 1 c 2 ? ? ? ? =a 1 (b 2 c 3 ? b 3 c 2 )? a 2 (b 1 c 3 ? b 3 c 1 ) + a 3 (b 1 c 2 ? b 2 c 1 ) Example 1 1. ? ? ? ? ?1 2 3 5 ? ? ? ? = ?5? 6 = ?11 2. ? ? ? ? ? ? 2 4 6 ?1 3 5 7 2 6 ? ? ? ? ? ? = 2 ? ? ? ? 3 5 2 6 ? ? ? ? ? 4 ? ?

## Need Help?

We hope your visit has been a productive one. If you're having any problems, or would like to give some feedback, we'd love to hear from you.

For general help, questions, and suggestions, try our dedicated support forums.

If you need to contact the Course-Notes.Org web experience team, please use our contact form.

## Need Notes?

While we strive to provide the most comprehensive notes for as many high school textbooks as possible, there are certainly going to be some that we miss. Drop us a note and let us know which textbooks you need. Be sure to include which edition of the textbook you are using! If we see enough demand, we'll do whatever we can to get those notes up on the site for you!