The dot product and cross product

The dot product and cross product

Post by Jacky Lu » Fri, 04 Mar 2005 17:13:23


Please correct me if this is wrong
According to my interpretation of the dot product and cross product from the
book 3d math primer, dot product will allow us to tell if the 2 vectors form
an acute, right or obtuse angle. And from the cross product, we get the
normal of a plane. Could anyone here elaborate this concept, the book gives
me a full stop at this point. Thanks a lot
Jack
 
 
 

The dot product and cross product

Post by Robi » Fri, 04 Mar 2005 18:56:06

the dot product is equal to the cosine of the smallest angle between two
vectors multiplied by the lengths of the 2 vectors.

the cross product gives you a vector which is perpendicular to both vectors,
the direction will depend on the order. A X B = - B X A. Using the left
hand rule you place your left hand open with your fingers in the direction
of the first vector, then curl your fingers toward the second vector, your
thumb
will point in the direction of the resulting vector.
The length of the crossproduct result is equal to the sine of the smallest
angle between the two vectors multiplied by the lengths of the two vectors.

Robin



XXXX@XXXXX.COM ...

 
 
 

The dot product and cross product

Post by Jacky Lu » Fri, 04 Mar 2005 19:32:46

Hi Robin,
The usages are practically correct as well?
Thanks a lot
Jack

"Robin" < XXXX@XXXXX.COM >
: XXXX@XXXXX.COM ...
vectors,
vectors.
 
 
 

The dot product and cross product

Post by Robi » Fri, 04 Mar 2005 21:34:29

Yes,

since the dot product can given you cosine of the angle, you can use
arccosine and determine the angle between 0 and 180 degrees, ie 0<=acute<90,
right==90 or 90<obtuse<=180

since a plane can be defined by two non colinear vectors, the cross product
will give you a vector normal to it.

Robin



% XXXX@XXXXX.COM ...
 
 
 

The dot product and cross product

Post by Eyal Tele » Sat, 05 Mar 2005 06:57:21

Google is your friend.

Eyal