Hello,
(see picture)
could you explain which is correct way to transform first expression into vectors (a or b) and why?
Thank you
If $\displaystyle R$ is the vector from $\displaystyle q_1$ to $\displaystyle q_2$ whose length is 1, then the correct expression is (b). This is because $\displaystyle a$ is the angle between $\displaystyle R$ and $\displaystyle u$, and $\displaystyle b$ is the angle between $\displaystyle R$ (plotted from $\displaystyle q_2$) and $\displaystyle v$, so $\displaystyle (\vec{R}\cdot\vec{u})=Ru\cos a =u\cos a$ and $\displaystyle (\vec{R}\cdot\vec{v})=Rv\cos b =v\cos b$. Dot product uses the angle between the two vectors. If the length of $\displaystyle R$ is not 1, then one has to divide by $\displaystyle R^2$ (in addition to the division by $\displaystyle c^2$).