I need some advice on how to approach this problem -
I have one vector and its components given a particular frame of reference ($A_x,\, A_y,\, A_z$). I have a second vector's components that is computed in a different frame of reference ($B_x,\,B_y,\,B_z$) and I need the dot product between these two vectors. I can't simply take the dot product (i.e.,$\mathbf A\cdot\mathbf B=A_xB_x+A_yB_y+A_zB_z$) because the two vector's components are computed with different orientations in mind.
Given that there is no way to orient one vector to match the frame of reference of the other vector, is there a way I can still get a dot product?