高一数学，平面向量
\u9ad8\u4e2d\u6570\u5b66 \u5e73\u9762\u5411\u91cf \u516c\u5f0f\u5927\u5168\u4e00\u3001\u5e73\u9762\u5411\u91cf\u516c\u5f0f\uff1a\u8bbea=\uff08x\uff0cy\uff09\uff0cb=\uff08x'\uff0cy'\uff09\u3002
1\u3001\u5411\u91cf\u7684\u52a0\u6cd5
\u5411\u91cf\u52a0\u6cd5\u7684\u8fd0\u7b97\u5f8b\uff1a
\u4ea4\u6362\u5f8b\uff1aa+b=b+a\uff1b
\u7ed3\u5408\u5f8b\uff1a\uff08a+b\uff09+c=a+\uff08b+c\uff09
2\u3001\u5411\u91cf\u7684\u51cf\u6cd5
\u5982\u679ca\u3001b\u662f\u4e92\u4e3a\u76f8\u53cd\u7684\u5411\u91cf\uff0c\u90a3\u4e48a=-b\uff0cb=-a\uff0ca+b=0\u30020\u7684\u53cd\u5411\u91cf\u4e3a0
AB-AC=CB\u3002\u5373\u201c\u5171\u540c\u8d77\u70b9\uff0c\u6307\u5411\u88ab\u51cf\u201d
a=\uff08x\uff0cy\uff09b=\uff08x'\uff0cy'\uff09\u5219a-b=\uff08x-x'\uff0cy-y'\uff09
\u4e8c\u3001\u5e73\u9762\u5411\u91cf\uff0c\u5782\u76f4\uff0c\u5e73\u884c\u5e73\u79fb\u7b49\u7684\u5173\u7cfb\uff1a
\u4e09\u70b9\u5171\u7ebf\u5b9a\u7406
\u82e5OC=\u03bbOA +\u03bcOB ,\u4e14\u03bb+\u03bc=1 ,\u5219A\u3001B\u3001C\u4e09\u70b9\u5171\u7ebf
\u4e09\u89d2\u5f62\u91cd\u5fc3\u5224\u65ad\u5f0f
\u5728\u25b3ABC\u4e2d\uff0c\u82e5GA+GB+GC=O\uff0c\u5219G\u4e3a\u25b3ABC\u7684\u91cd\u5fc3
\u5411\u91cf\u5171\u7ebf\u7684\u91cd\u8981\u6761\u4ef6
\u82e5b\u22600\uff0c\u5219a//b\u7684\u91cd\u8981\u6761\u4ef6\u662f\u5b58\u5728\u552f\u4e00\u5b9e\u6570\u03bb\uff0c\u4f7fa=\u03bbb\u3002
a//b\u7684\u91cd\u8981\u6761\u4ef6\u662fxy'-x'y=0\u3002
\u96f6\u5411\u91cf0\u5e73\u884c\u4e8e\u4efb\u4f55\u5411\u91cf\u3002
\u5411\u91cf\u5782\u76f4\u7684\u5145\u8981\u6761\u4ef6
a\u22a5b\u7684\u5145\u8981\u6761\u4ef6\u662fa•b=0\u3002
a\u22a5b\u7684\u5145\u8981\u6761\u4ef6\u662fxx'+yy'=0\u3002
\u96f6\u5411\u91cf0\u5782\u76f4\u4e8e\u4efb\u4f55\u5411\u91cf\u3002
\u6bd4\u8f83\uff1a
\u5171\u7ebf\u5411\u91cf\u4e0e\u5e73\u884c\u5411\u91cf\u5173\u7cfb
\u7531\u4e8e\u4efb\u4f55\u4e00\u7ec4\u5e73\u884c\u5411\u91cf\u90fd\u53ef\u79fb\u5230\u540c\u4e00\u76f4\u7ebf\u4e0a\uff0c\u6545\u5e73\u884c\u5411\u91cf\u4e5f\u53eb\u505a\u5171\u7ebf\u5411\u91cf\u3002
\u5e73\u884c\u5411\u91cf\u4e0e\u76f8\u7b49\u5411\u91cf\u7684\u5173\u7cfb
\u76f8\u7b49\u7684\u5411\u91cf\u4e00\u5b9a\u5e73\u884c\uff0c\u4f46\u662f\u5e73\u884c\u7684\u5411\u91cf\u5e76\u4e0d\u4e00\u5b9a\u76f8\u7b49\u3002\u4e24\u4e2a\u5411\u91cf\u76f8\u7b49\u5e76\u4e0d\u4e00\u5b9a\u8fd9\u4e24\u4e2a\u5411\u91cf\u4e00\u5b9a\u8981\u91cd\u5408\u3002\u53ea\u7528\u8fd9\u4e24\u4e2a\u5411\u91cf\u957f\u5ea6\u76f8\u7b49\u4e14\u65b9\u5411\u76f8\u540c\u5373\u53ef\u3002\u5176\u4e2d\u201c\u65b9\u5411\u76f8\u540c\u201d\u5c31\u5305\u542b\u7740\u5411\u91cf\u5e73\u884c\u7684\u542b\u4e49\u3002
|a|=1\uff0c|b|=2\uff0c=\u03c0/3
\u6545\uff1aa\u00b7b=1*2*cos(\u03c0/3)=1
\u5145\u5206\u6027\uff1a
m=1\uff0c(a-mb)\u00b7a=|a|^2-ma\u00b7b=1-a\u00b7b
=1-1=0\uff0c\u6545\uff1a(a-mb)\u22a5a
\u5145\u5206\u6027\u6210\u7acb
\u5fc5\u8981\u6027\uff1a
(a-mb)\u22a5a\uff0c\u5373\uff1a(a-mb)\u00b7a=|a|^2-ma\u00b7b
=1-m=0\uff0c\u5373\uff1am=1
\u5fc5\u8981\u6027\u6210\u7acb
\u6545\u662f\u5145\u8981\u6761\u4ef6\uff0c\u9009C
同理：向量CF=2/3向量CB+1/3向量CA 向量BE=2/3向量BA+1/3向量BC
所以向量AD+向量BE+向量CF=1/3CB=-1/3BC
所以选A
绛旓細鏈夋柟鍚戞湁澶у皬鐨勯噺鍙仛 (缁忓吀) 鍚戦噺, 鍙互鐢ㄦ湁鍚戠嚎娈靛嚑浣曞湴琛ㄧず, 涔熷彲浠ョ敤涓缁勫熀浣滃睍寮鍚庣敤涓涓暟缁勪唬鏁板湴琛ㄧず, 涔熷彲浠ョ敤鍏充簬涓缁勫熀鐨勭嚎鎬у睍寮寮忎唬鏁板湴琛ㄧず. 鍦ㄧ墿鐞嗕腑鐨勪緥瀛愭湁閫熷害, 浣嶇Щ, 鐢靛満寮哄害, 纾佸満寮哄害绛夌瓑. 濡傛灉涓涓悜閲忓彲浠ュ湪 n 缁寸┖闂磋涓, 灏卞彨 n 缁村悜閲. 骞抽潰鍚戦噺鏄寚 2 缁村悜閲....
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绛旓細瑙ｇ瓟锛殀a+b|=1,鍚戦噺a+b骞宠浜嶺杞 鎵浠 a+b=(1,0)鎴朼+b=(-1,0)鈶 a+b=(1,0)a=(a+b)-b=(1,0)-(2,-1)=(-2,1)鈶 a+b=(-1,0)a=(a+b)-b=(-1,0)-(2,-1)=(-3,1)
绛旓細璁綼=xb+yc 鈭礱锛濓紞e1锛3e2锛宐锛4e1锛2e2锛宑锛濓紞3e1锛12e2 鈭-e1+3e2=x(4e1锛2e2)+y(锛3e1锛12e2)=(4x-3y)e1+(2x+12y)e2 鈭礶1鍜宔2涓嶅叡绾挎牴鎹骞抽潰鍚戦噺鍩烘湰瀹氱悊 鈭磠4x-3y=-1 {2x+12y=3 瑙ｅ緱锛歺=-1/18,y=7/27 鈭碼=-1/18*b+7/27*c ...
绛旓細鍔犳硶 1銆佷笁瑙掑舰娉曞垯 2銆佸钩琛屽洓杈瑰舰娉曞垯 璁綼鍚戦噺=锛坸1,y1),b鍚戦噺=锛坸2,y2),鍒欙細a鍚戦噺+b鍚戦噺=锛坸1+x2,y1+y2)鍑忔硶 涓夎褰㈡硶鍒欙細璁綼鍚戦噺=锛坸1+y1),b鍚戦噺=锛坸2,y2),鍒欙細a鍚戦噺+b鍚戦噺=锛坸1-x2,y1-y2)a鍚戦噺*b鍚戦噺=b鍚戦噺*a鍚戦噺 鍙傝冭祫鏂欙細111褰潳 ...
绛旓細= |a|^2 + |b|^2 + |c|^2 + 2a*b + 2c*(a+b) = 0 3^2 + 5^2 + 7^2 + 2a*b + 2c*(-c) = 3^2 + 5^2 - 7^2 + 2a*b = 0 a*b = 15 = |a||b| cos = 3*5*cos cos = 1 鍚戦噺a涓巄鐨勫す瑙 = 90 degree ...
