如图,在三棱锥S-ABC中,SC⊥平面ABC,点P、M分别是SC和SB的中点,设PM=AC=1,∠ACB=90°,直线AM与直线S
\u5982\u56fe\uff0c\u5728\u4e09\u68f1\u9525S\u2014ABC\u4e2d\uff0cSC\u22a5\u5e73\u9762ABC\uff0c\u70b9P\u3001M\u5206\u522b\u662fSC\u548cSB\u7684\u4e2d\u70b9\uff0c\u8bbePM=AC=1\uff0c\u2220ACB=90\u00b0\uff0c\u76f4\u7ebfAM\u4e0e\u76f4\u7ebf\uff08I\uff09\u89c1\u89e3\u6790\uff08\u2161\uff09\u89c1\u89e3\u6790\uff08 \u2162\uff09 \u672c\u8bd5\u9898\u4e3b\u8981\u662f\u8003\u67e5\u4e86\u7a7a\u95f4\u4e2d\u70b9\u7ebf\u9762\u7684\u4f4d\u7f6e\u5173\u7cfb\u7684\u7efc\u5408\u8fd0\u7528\u3002\uff081\uff09\u70b9P\u3001M\u5206\u522b\u662fSC\u548cSB\u7684\u4e2d\u70b9 \u2234 \u53c8 \u2234 \uff082\uff09\u5efa\u7acb\u7a7a\u95f4\u76f4\u89d2\u5750\u6807\u7cfbC\u2014xyz.\uff0c\u501f\u52a9\u4e8e\u6cd5\u5411\u91cf\u7684\u5782\u76f4\u95ee\u9898\u6765\u8bc1\u660e\u9762\u9762\u7684\u5782\u76f4\u3002\uff083\uff09\u5728\u7b2c\u4e8c\u95ee\u7684\u57fa\u7840\u4e0a\u53ef\u77e5\u5f97\u5230\u5e73\u9762\u7684\u6cd5\u5411\u91cf\u4e0e\u6cd5\u5411\u91cf\u7684\u5939\u89d2\uff0c\u5f97\u5230\u4e8c\u9762\u89d2\u7684\u5e73\u9762\u89d2\u7684\u5927\u5c0f\u3002\u89e3\uff1a\uff08I\uff09\u2235\u70b9P\u3001M\u5206\u522b\u662fSC\u548cSB\u7684\u4e2d\u70b9 \u2234 \u53c8 \u2234 \uff08II\uff09\u2235SC\u22a5\u5e73\u9762ABC\uff0cSC\u22a5BC\uff0c\u53c8\u2235\u2220ACB=90\u00b0\u2234AC\u22a5BC\uff0cAC\u2229SC=C\uff0cBC\u22a5\u5e73\u9762SAC\uff0c \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.2\u5206\u53c8\u2235P\uff0cM\u662fSC\u3001SB\u7684\u4e2d\u70b9\u2234PM\u2225BC\uff0cPM\u22a5\u9762SAC\uff0c\u2234\u9762MAP\u22a5\u9762SAC\uff0c\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026..5\u5206\uff08II\uff09\u5982\u56fe\u4ee5C\u4e3a\u539f\u70b9\u5efa\u7acb\u5982\u56fe\u6240\u793a\u7a7a\u95f4\u76f4\u89d2\u5750\u6807\u7cfbC\u2014xyz. \u5219 \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026\u20269\u5206\u8bbe\u5e73\u9762MAB\u7684\u4e00\u4e2a\u6cd5\u5411\u91cf\u4e3a \uff0c\u5219\u7531 \u53d6z= \u2026\u2026\u2026\u2026\u2026\u2026\u2026..11\u5206\u53d6\u5e73\u9762ABC\u7684\u4e00\u4e2a\u6cd5\u5411\u91cf\u4e3a \u5219 \u6545\u4e8c\u9762\u89d2M\u2014AB\u2014C\u7684\u4f59\u5f26\u503c\u4e3a \u2026\u2026\u2026\u2026\u2026\u2026\u2026\u2026.13\u5206
\u8bc1\u660e\uff1a\uff081\uff09\u2235SC\u22a5\u5e73\u9762ABC\uff0cSC\u22a5BC\uff0c\u53c8\u2235\u2220ACB=90\u00b0\u2234AC\u22a5BC\uff0cAC\u2229SC=C\uff0cBC\u22a5\u5e73\u9762SAC\uff0c\u53c8\u2235P\uff0cM\u662fSC\u3001SB\u7684\u4e2d\u70b9\u2234PM \u2225 BC\uff0cPM\u22a5\u9762SAC\uff0c\u2234\u9762MAP\u22a5\u9762SAC\uff0c\uff085\u5206\uff09\uff082\uff09\u2235AC\u22a5\u5e73\u9762SAC\uff0c\u2234\u9762MAP\u22a5\u9762SAC\uff0e\uff083\u5206\uff09\u2234AC\u22a5CM\uff0cAC\u22a5CB\uff0c\u4ece\u800c\u2220MCB\u4e3a\u4e8c\u9762\u89d2M-AC-B\u7684\u5e73\u9762\u89d2\uff0c\u2235\u76f4\u7ebfAM\u4e0e\u76f4\u7ebfPC\u6240\u6210\u7684\u89d2\u4e3a60\u00b0\u2234\u8fc7\u70b9M\u4f5cMN\u22a5CB\u4e8eN\u70b9\uff0c\u8fde\u63a5AN\uff0c\u5219\u2220AMN=60\u00b0\u5728\u25b3CAN\u4e2d\uff0c\u7531\u52fe\u80a1\u5b9a\u7406\u5f97 AN= 2 \uff0e\u5728Rt\u25b3AMN\u4e2d\uff0c AM= AN tan\u2220AMN = 2 ? 3 3 = 6 3 \uff0e\u5728Rt\u25b3CNM\u4e2d\uff0c tan\u2220MCN= MN CN = MN CN = 6 3 1 = 6 3 \u6545\u4e8c\u9762\u89d2M-AC-B\u7684\u6b63\u5207\u503c\u4e3a 6 3 \uff0e\uff085\u5206\uff09
(1)证明:∵P,M是SC、SB的中点∴PM∥BC,
∵BC?面AMP,PM?面AMP
∴BC∥面AMP;
(2)证明:∵SC⊥平面ABC,SC⊥BC,
又∵∠ACB=90°∴AC⊥BC,
∵AC∩SC=C,∴BC⊥平面SAC,
∵PM∥BC,
∴PM⊥面SAC,
∵PM?面MAP,∴面MAP⊥面SAC;
(3)解:以C为原点,建立空间直角坐标系,
则P(0,0,
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