How to multiply vector by quaternion ?
Hey masloed.
I'm not sure what you mean by this, but perhaps you could find an interpretation by multiplying two quaternions with the scalar part corresponding to your vector being equal to zero.
In fact, if you set the scalar part of a quaternion to zero, the vector part will be the cross product and the scalar part will be the negative of the dot product which produces a representation of the bi-vector in the Geometric Algebraic product.