Lorentz Force Equation: Geometric Interpretation

[Somefantastik]

$$\textbf{L} \ = \ q\left( \textbf{v \ x \ B} \right)$$

L, v, and B are vectors, and B represents magnetic induction.

if $$\textbf{v} \ = \widehat{x},$$
then $$\textbf{v x B} = \widehat{x} \ \textbf{x B}$$

What is this quantity, $$\widehat{x} \ \textbf{x B}$$, geometrically?

 

[Hepth]

A vector orthogonal to both x and B whose magnitude corresponds to the amount of angle needed to rotate B into the x direction times the magnitude of B itself.
The magnitude is also the area of a rhombus framed by the vectors.

 

[Somefantastik]

Can I find B if I know

$$\widehat{x} \textbf{ x B}$$

$$\widehat{y} \textbf{ x B}$$

$$\widehat{z} \textbf{ x B}$$ ?