[b]解法一  [/b]（参考 Euler 角）将已知方程写成[tex=9.357x2.786]hl1bmR6Xjco8Mi5B11/ctz/cnzh53kOheFLwwn/CmJw6ZPT9od6vnmxl6lwBZoxZ[/tex]，利用平移[tex=2.214x1.143]qMUtDz4co1/IUd/w/7sHIA==[/tex]，[tex=3.714x2.357]0Xwg6hVuxtlgZkmvOJvY8bMC6oPUFeCC0jP222zJsoY=[/tex]，[tex=2.0x1.143]IgGLgyfxYE8Sjnr8fWoFRw==[/tex]，可得[p=align:right][tex=6.643x1.357]I/dVu8g6R5UedAHO8SoZhFXd3yMSb6RQA6utDcaah6swZpDa3WrscZ6y/PDAryrU[/tex].                                （1）取直线[tex=6.429x2.929]7EJHVCtO2IWq3KpdB+jQslRxmDcA1mcozZf+FiGzDkJbR7eiFDtLalMnUbaSCwdOElct7svDZBVcvcPJi6GAEWblxFe5O1nVlnqXzDVkQDoI4Kvoud9WyWW8fXUspwnp[/tex]为新[tex=1.0x1.143]uDURn6KTVSzuxHB9PQPJUjgZCNfuZ+E4cktMixAfUQc=[/tex]轴，即绕[tex=0.786x1.143]Ex2vqmY4XQXLlfB9Do9iaQ==[/tex]轴旋转[tex=0.5x1.0]qm+hGi0qngLh1B7HsENMPg==[/tex]角，其中[tex=0.5x1.0]qm+hGi0qngLh1B7HsENMPg==[/tex]满足[tex=4.571x2.357]MD+CHS0JGJr8swFQQ1HCJgbYb0FA4N6aW+GapL8BmdE=[/tex]，旋转变换为[p=align:center][tex=10.357x4.5]7EJHVCtO2IWq3KpdB+jQsrB6api6XTiW4A20y5aW7YwOvqkkIAkJoxRWPQK0LBMR/mihAF91HdjklSgbupMgHNDSOaD4RafIzPvgmHOfy/W2zM2cjtyAukV3BroKsAl5U9aXYt+tMW14vOMBLGtTkXPMveyd5el5wynturZmbMHQAIAkWngCXdDi8W84bua9apj8tQz77vnUemw622+go/oGfdFD30gNnrQIu0K8cBvBi1JhzKUbuD7CMYoq1h3EokA/v1NR7HGuH0glDRqRVMzPKLnEzLIvHRBN9Hxgcag=[/tex]，代入（1）得[p=align:right][tex=7.143x1.5]vNGTU779IEL2Ffk4wgbXo5G+3go6kZ7MC5ipn1hiTOy9jQ0IP08XFXxa3t1tRyzHsRmq70KfCWPomf68udVniw==[/tex].                              （2）再取旋转角[tex=0.714x1.0]OqF+/h/mAb1/2XhJuj27xg==[/tex]，使其满足[tex=5.357x2.643]V1SjnAVIAwWtjCli7rKzPswvn6eGQV6SUdnvICJOzAucEtepJ20eFEM7MXAuULyz[/tex]，经过绕[tex=1.0x1.143]uDURn6KTVSzuxHB9PQPJUjgZCNfuZ+E4cktMixAfUQc=[/tex]轴旋转[tex=0.714x1.0]OqF+/h/mAb1/2XhJuj27xg==[/tex]角的变换：[p=align:center][tex=10.786x4.5]7EJHVCtO2IWq3KpdB+jQsrB6api6XTiW4A20y5aW7YwJbvUEbRe0eie7WXS3ADvvSAcCVtvDrG7ZnLDvJorZxSxRQAVuj6dkIDhPiAS+Lxv2+lbi74sW8L8XHV2Ovfe8oWudI8hN/ASM6yLH+vSUqHw6gIU5DSjRKy3Q/eZrYrxsxXZFECkbUq0mbiyFjtpBLYbALmlpvDIGfM7B82ncrBmosKnoT8NSPwGge+vylwJoasyywDs4euE3tTM2f8ON[/tex]，就得到[tex=2.214x1.071]DVrgPDJ20zwhaHNwCuYehw==[/tex].以上三个变换的乘积就是所求变换.[b]解法二  [/b] 已知平面方程可化为[tex=9.357x2.786]2SkBlWbwjiDBBod4TxP807FXWju/jTEmJlv7GwbZ13S+yB2p0hdNyZM7JTI0ab+b[/tex]，具有单位向量[p=align:center][tex=13.5x2.714]FgMErMawA9mwj3YfYPraV3ayfgcxllJQJGritRjEqZLqT1YpuJkpKZgBNPvF1K3U41Qn2lhygTB7jabkHI6Nh55HRRlGPtT5Lo2McKarElU=[/tex].取与[tex=0.643x0.786]/he/ol8BkDuTTL9yMPtH4Q==[/tex]正交的单位向量[tex=6.0x2.714]PYZSmeZCw6xom/NZGwJdnmMRZUzOvLh8/w5cEotRioUDULh+HE3fkqzxWKflXiTp[/tex]，[tex=17.714x3.929]9RTetLxmelhjiPRP3d4TB1cXGZQ8ssWu5iaGL78KktePIC9rrTGFuNxCb9P7OshNWajo6saKGhKBaxTVFEi2YlfL5HisXfV79FOms60Inuld1fB5evPifSYGpiYWLs2hjpajhKy33kqaL2oUTmnMOviBv/CX9nJfKnFW3l73oOgaAKsaAmwx4r353uIqrSYU[/tex].在以[tex=5.071x2.786]xw2jC5/X8ey1i41UxRd7S/SIGVi0lhV7uqnX7h+8RuY=[/tex]为原点，以 [tex=4.143x1.357]yPhJXQIl8Vkkaabg35IZOBjFSuT2/W/B9GA6Fqb3AMeRc0u9oePLuHIPnovlUIp8[/tex]为基向量组的坐标系下，原平面方程即化为[tex=2.071x1.143]KvLybXIZhVJ1Zh9APBkepA==[/tex]，其中[tex=17.857x3.357]MvtHC7hiwLteallCqj2vBjwBi4h3iX56XlVkJgmJyruEcmfgGVw5O8hGqTZy6veMybFDqLe8GBBh4STiDFHuIVeHTCl2uzm84yfUkE8KDfMDYrLDWTsXCX/yKoNxxpK+guwBaBXhl1uM9cKujhazUVZwZ5ggXaIoTn0/nZN0z98hXkKjW53/72H67PxqhcFh4vHzm3foqU9KPrDT0ad6lQ==[/tex].[b]解法三  [/b] 令[tex=23.714x2.643]U1OXxq0wYVb7UCAHR81xo2o5QnWyZuqo3bwAIRt1A20Dd3hII7Rsk7p6S9KPsFxcPV1vZS0FDsjfPjIOxzyFsV5cmLFNz3Ex8NgaP6vVaJuTTLu2scFQxMWigqmd8w/Ta9aHXYlFDRlWUrjxDUddpQ==[/tex].取两个互相垂直的单位向量[tex=0.857x1.0]NE5viVQtUJ1Z7sNTvKYsYg==[/tex]，[tex=0.857x1.0]iB1uBost/kvxcpYUJQ/2SA==[/tex]使它们都与向量[tex=4.786x1.357]KY0d3bTe6gM42HYpZ92rcA==[/tex]垂直，并且使[tex=0.857x1.0]6w3s5yvU+YGAbD8PTHecIg==[/tex]，[tex=0.857x1.0]8KujEsbM8zTzbA+hMPr8XQ==[/tex]，[tex=0.857x1.0]IO8KINLIzoztXQnBtukeQw==[/tex]是右手系. 比如可取[tex=7.5x2.643]rIyib7kNlR/VZNZ3CnkDIJrab+gkWTF91GFEgE/Rj5T+/XfxOYRuoisqDn0Xxge1[/tex]，[tex=13.429x2.643]4VQwG6XTRf73xkQ4HopjNgst6hE05/mui02N//s6nYdC8eVgYxJm2AptFDgz4hzqwzOEiWzTetJjkkHCIMReBA==[/tex].令[tex=6.643x2.643]RFCEJudsCzx/VIvETT7BylEkMG1FSUDXul/bqlF7klb6wsHIVAQE7t43KKo58G4P[/tex]，[tex=1.571x1.357]MZ5LZumd6Qbi+TmXYuljuA==[/tex][tex=9.5x2.643]A9/Zfy8ZBoH1sbiuu4b/sOzbBfdqjEASi5CD/jwvNHtcivmnud7OAKv+i4ikHvY7[/tex]即可.