3. As shown in Figure 1, in the cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, points $E$ and $F$ are on $A B_{1}$ and $B C_{1}$ respectively (not coinciding with the endpoints of the segments), and $A E=B F$. Then, among the following 4 conclusions:
(1) $A A_{1} \perp E F$; (2) $A_{1} C_{1} / / E F$; (3) $E F / /$ plane $A_{1} B_{1} C_{1} D_{1}$; (4) $E F$ and $A_{1} C_{1}$ are skew.
The correct ones are ( ).
(A)(2)(4) (B)(1)(4) ( C)(2)(3) (D)(1)(3)
3.D.

As shown in Figure 2, draw $E P \perp A B$ at point $P$, $F Q \perp B C$ at point $Q$, and connect $P Q$. It is easy to see from the given conditions that $P E \xlongequal{\|} Q F$.

Since $P E \perp$ plane $A C$, then $P E \perp P Q$, which means quadrilateral $P E F Q$ is a rectangle.

Therefore, $A A_{1} \perp E F$, $E F / /$ plane $A C$, i.e., $E F / /$ plane $A_{1} C_{1}$. Hence (1) and (3) are correct.