Vector Product Consider two vectors,

AandB,We can

definea new vectorC,C=AxBThe magnitude of C is

C = A B sin or

|C| = |A| |B| sin where is the angle between vectors

AandB.Remember, tho', that

Cis avector. ThedirectionofCisperpendicularto the plane define by vectorsAandB. That is,CAand

CBBut that still leaves

twopossibilities for the direction of vectorC. To find a single, unique direction, we shall employ (or invent) theright-hand rule.The right hand rule:

With the fingers of your right hand, rotate the first vector A into the second vector B. The direction your thumb points is the direction of the new vector C.(In this example, vectorsAandBare in the plane of this page or screen and the new vectorCpointsintothe page or screen)

Vector products(also called"cross products") always involve three-dimensional visualizations. For our example here, if vectorsAandBlie in the plane of the screen, then vectorCis pointingintothe screen.Notice that this vector product is

notcommutative.D=BxAIn fact, the cross product (or vector product) is anti-commutative; that is,

AxB= -BxAWith this basic definition of the vector product, what can we do with vectors

AandBwritten in component ori,j,knotation?A= A_{x}i+ A_{y}j+ A_{z}k

B= B_{x}i+ B_{y}j+ B_{z}k

Rolling MotionTorqueReturn to ToC, Ch11, Rolling Motion(c) Doug Davis, 2001; all rights reserved