Cross Product for Biot-Savart Derivation of Current Loop Biot-Savart's law can be used to determine the magnetic field produced by a figure at a point. Introductory physics texts integrate $dB$ to obtain $B$ where
$$dB = \frac{I\mu_{0}}{4\pi  r^2}  dl \times \frac{r}{\lVert \mathbf{r} \rVert}$$
where $I$ and $\mu_{0}$ are constants.
Here, $dl$ and $r$ ($\frac{r}{\lVert \mathbf{r} \rVert}$ might as well be $r$ for this comparison) make an angle. The angle of interest is formed by the intersection of $r$ (in the diagram) and $dl$. My textbooks claim that the angle is $90$. I don't see how. 


Up to a rotation around the $\hat x$ axis, you can always represent the punctual situation as you did in your drawing.
Now: $\hat r$ lies in the plane of the sheet of paper (the one spanned by the radius $\vec R$ and by $\hat x$), while $d\vec l$ is perpendicular to the sheet of paper. Hence, to all the vectors lying in it.
