Vector and Scalar Triple Products                                

 

 

In a Nut Shell:  The vector product of two vectors results in a new vector

perpendicular to the original two vectors.  The direction of the new vector is

conveniently determined using the “right hand rule”. 

 

For a rectangular coordinate system point the fingers of your right hand in the direction of

the x-axis.  Then  rotate your fingers towards the y-axis.  The result of a vector product is

another vector (your thumb) perpendicular to the two original vectors (along the z-axis).

 See the figure below.

 

 

                            

 

The vector product, also called the cross product,  of  U  =  (u1,u2,u3) and

of   V  =  (v1, v2, v3)  is define by the 3 x 3 determinant below as:

                                               i            j          k

 

            U   x   V   =   det        u1           u2         u3  

                            

                                              v1           v2         v3  

 

   with  i  , j ,  k  in the first row  u1,    u2,   u3  in the second row, and  v1,    v2,   v3   in the third row

 

                    

 

Click here to continue with vector products.

 



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