46. In space, a line $l$ and points $A$ and $B$ are given, such that lines $A B$ and $l$ are skew. Find a point $M$ on line $l$ such that the sum of the distances $|A M|+|M B|$ is minimized.
46. By rotating around the axis $l$, we will translate point $B$ into the plane passing through point $A$ and line $l$, and do so in such a way that points $A$ and $B^{\prime}$ - the image of $B$ - are on opposite sides of line $l$. The shortest path from $A$ to $B^{\prime}$ is the segment $A B^{\prime}$, intersecting $l$ at point $M$. Any other point $N \in l$ gives a path of length $|A N|+\left|N B^{\prime}\right|>\left|A B^{\prime}\right|$. Since $\left|M B^{\prime}\right|=|M B|$, point $M$ is the desired one.