Maths - Vectors - Forum discussion Paolo

By: Nobody/Anonymous - nobody
RE: Vector division  
2005-06-06 10:04

In this page: https://www.euclideanspace.com/maths/algebra/vectors/  
In the paragraph about "Vector Division" there's a misleading drawing. The sentence describing it is also misleading. 
Let's call C the result of AxB. Let's call B' any possible vector contained in the plane normal to C, except those parallel to A.  
It is not always true that AxB'=C. On the contrary, the sentence describing the drawing and the drawing are ambiguous and seem to suggest that AxB'=C is always true. 
Actually, AxB'=C is true only if the component of vector B' normal to A is equal to the component of vector B normal to A (let's call it Bnormal). I.e., |B| * sin(theta) must be equal to |B'| * sin(theta') = |Bnormal|, where theta and theta' are the oriented angles from A to B and from A to B'.  
Graphically, it interesting to show that all of these B' vectors have their tip on a line parallel to A and passing through the tip of B. 
 
Regards, 
Paolo DL