$解:如答圖②，當(dāng)0\lt a≤3時(shí)$
$∵點(diǎn)P與點(diǎn)P_{1}關(guān)于y軸對(duì)稱(chēng),P(-a,0),∴P_{1}(a,0)$
$設(shè)P_{2}(x_{1},0),又∵點(diǎn)P_{1}與點(diǎn)P_{2}關(guān)于直線l對(duì)稱(chēng)$
$∴\frac{x_{1}+a}{2}=3，即x_{1}=6-a$
$∴P_{2}(6-a,0),則P_{1}P_{2}=6-a-a=6-2a$
$如答圖③當(dāng)a＞3時(shí)$
$∵點(diǎn)P與點(diǎn)P_{1}關(guān)于y軸對(duì)稱(chēng),P(-a,0),∴P_{1}(a,0)$
$設(shè)P_{2}(x_{2},0),又∵點(diǎn)P_{1}與點(diǎn)P_{2}關(guān)于直線l對(duì)稱(chēng)$
$∴\frac {x_{2}+a}{2}=3,即x_{2}=6-a$
$∴P_{2}(6-a,0)$
$則P_{1}P_{2}=a-(6-a)=2a-6$
$綜上所述，當(dāng)0\lt a≤3時(shí),P_{1}P_{2}=6-2a$
$當(dāng)a＞3時(shí)，P_{1}P_{2}=2a-6$
