Cross Product Angle: 0 to π or ACW from a to b?

[PFuser1232]

When we talk about the angle between two vectors while computing the cross product, which angle are we referring to exactly? According to most sources, the angle should be between 0 and π; yet according to my math book, "the angle is measured in an anticlockwise sense from a to b, if the vector product a x b is to be computed."

 

[SteamKing]

When we talk about the angle between two vectors while computing the cross product, which angle are we referring to exactly? According to most sources, the angle should be between 0 and π; yet according to my math book, "the angle is measured in an anticlockwise sense from a to b, if the vector product a x b is to be computed."

How about this:

http://www.mathsisfun.com/algebra/vectors-cross-product.html

Scroll down a ways to see the diagram of the angle.

 

[Matterwave]

The trigonometric function occurring in the cross product is sine. Notice that sin(360-x)=sin(-x)=-sin(x) so notice that the only thing that changes whether you measure the small angle or the big angle is that you change the sign. For that issue, just follow the right hand rule. :)

 

[PFuser1232]

So I should use the smaller angle, and use the right hand rule, right?
I don't understand why my math book had to specify the "orientation" of the angle.

 

[lurflurf]

$$a\times b=-b\times a$$

Some books like yours allow the angle to be positive or negative. Other books use only positive angles and use the right hand rule to establish direction.