the cross product

• Mar 21st 2010, 07:23 PM
needmathhelptoujours
the cross product
i wasn't @ school the day we learned the cross product.
heres my first question, just help me get this one so i can complete the worksheet please!!!

<-8,13,-2> X <-2,19,1>
• Mar 21st 2010, 09:25 PM
Quote:

Originally Posted by needmathhelptoujours
i wasn't @ school the day we learned the cross product.
heres my first question, just help me get this one so i can complete the worksheet please!!!

<-8,13,-2> X <-2,19,1>

Do you know how to find determinants? There isn't really anything fancy to understand, the cross product is just a defintion.

If "a" and "b" are the vectors:

\$\displaystyle a=<a_1,a_2,a_3>\$
\$\displaystyle b=<b_1,b_2,b_3>\$

The cross-product is the vector defined by:

\$\displaystyle a X b=<a_2b_3-a_3b_2,a_3b_1-a_1b_3,a_1b_2-a_2b_1>\$

This is difficult to remember, it's best if you know how to find determinants.

http://en.wikipedia.org/wiki/Cross_product

If you scroll down to "matrix" notation, you'll see how the determinant definition makes 3-by-3 cross products a little easier to remember.