CN-LEAGUE 1997 Problem 2

In regular tetrahedron $ABCD$ , $E\in AB,F\in CD$ , satisfying: $\frac{|AE|}{|EB|}=\frac{|CF|}{|FD|}=\lambda(\lambda\in R_+)$ . Note that $f(\lambda)=\alpha_{\lambda}+\beta_{\lambda}$ , where $\alpha_{\lambda}=<EF,AC>,\alpha_{\lambda}=<EF,BD>$ . $\text{(A)}$ $f(\lambda)$ increases in $(0,+\infty)$ $\text{(B)}$ $f(\lambda)$ decreases in $(0,+\infty)$ $\text{(C)}$ $f(\lambda)$ increases in $(0,1)$ , decreases in $(1,+\infty)$ $\text{(D)}$ $f(\lambda)$ is a fixed value in $(0,+\infty)$