1 / 7

axb

The Right Hand Rule. axb. b. a. Properties of the Cross Product . a x b = - b x a (c a )x b = c( a x b ) = a x(c b ) a x( b + c ) = a x b + a x c ( a + b )x c = a x c + b x c a . ( b x c ) = ( a x b ) . c a x( b x c ) = ( a . c ) b -( a . b ) c.

klaus
Download Presentation

axb

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. The Right Hand Rule axb b a

  2. Properties of the Cross Product • axb = -bxa • (ca)xb = c(axb) = ax(cb) • ax(b+c) = axb + axc • (a+b)xc = axc + bxc • a.(bxc) = (axb).c • ax(bxc) =(a.c)b-(a.b)c

  3. The so-called scalar triplea.(bxc) But recall that the components of (bxc) come from 2x2 determinants

  4. a.(bxc) A-ha! We have a quick way to compute this!

  5. V = |bxc| |a||cos( )|=|a.(bxc)| The Geometric InterpretationVolume of a parallelpiped bxc a h c b Volume = (Area of Base)*(height)

  6. Q. How can we use the cross product to determine if 3 vectors are coplanar (lie in the same plane)? • Determine if the volume of the • resulting parallelpiped is nonzero

  7. Example Do the following points lie in the same plane? A=(1,-1,2) B=(2,0,1) C=(3,2,0) D=(5,4,2)

More Related