高一数学平面向量
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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
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\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
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\u5411\u91cf\u5171\u7ebf\u7684\u91cd\u8981\u6761\u4ef6
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a//b\u7684\u91cd\u8981\u6761\u4ef6\u662fxy'-x'y=0\u3002
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\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
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|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
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\u6545\u662f\u5145\u8981\u6761\u4ef6\uff0c\u9009C
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....
绛旓細鈶ラ浂鍚戦噺涓庝换鎰忓悜閲忕殑鏁伴噺绉负0銆傚悜閲忔暟閲忕Н鐨勮繍绠楀緥 鈶翠氦鎹㈠緥锛歛路b=b路a 鈶垫暟涔樼粨鍚堝緥锛氾紙位a锛壜穊=位锛坅路b)=a路锛埼籦锛夆懚鍒嗛厤寰嬶細锛坅+b锛壜穋=a路c+b路c 骞抽潰鍚戦噺鏁伴噺绉殑鍑犱綍鎰忎箟 鈶犱竴涓悜閲忓湪鍙︿竴涓悜閲忔柟鍚戜笂鐨勬姇褰 璁疚告槸a銆乥鐨勫す瑙掞紝鍒檤b|cos胃鍙仛鍚戦噺b鍦ㄥ悜閲廰鐨勬柟鍚戜笂...
绛旓細楂樹腑鏁板骞抽潰鍚戦噺鐨勬暟閲忕Н鏁欐璁捐涓 銆婂钩闈㈠悜閲忔暟閲忕Н銆嬫暀瀛﹁璁 妗堜緥鍚嶇О 骞抽潰鍚戦噺鏁伴噺绉殑璁捐 涓诲浜 缁勫憳 璇炬椂 3璇炬椂 涓銆佹暀鏉愬唴瀹瑰垎鏋 骞抽潰鍚戦噺鏁伴噺绉槸浜烘暀鐗楂樹竴涓嬪唽绗簲绔犵鍏妭鍐呭,鏈妭璇炬槸浠ヨВ鍐虫煇浜涘嚑浣曢棶棰樸佺墿鐞嗛棶棰樼瓑鐨勯噸瑕佸伐鍏枫傚涔犳湰鑺傝鎺屾彙濂芥暟閲忕Н鐨勫畾涔夈佸叕寮忓拰鎬ц川,瀹冩槸鑰冩煡鏁板鑳藉姏鐨勪竴...
绛旓細楂樹竴鏁板骞抽潰鍚戦噺鐭ヨ瘑鐐 鍚戦噺锛氭棦鏈夊ぇ灏忥紝鍙堟湁鏂瑰悜鐨勯噺.鏁伴噺锛氬彧鏈夊ぇ灏忥紝娌℃湁鏂瑰悜鐨勯噺.鏈夊悜绾挎鐨勪笁瑕佺礌锛氳捣鐐广佹柟鍚戙侀暱搴.闆跺悜閲忥細闀垮害涓虹殑鍚戦噺.鍗曚綅鍚戦噺锛氶暱搴︾瓑浜庝釜鍗曚綅鐨勫悜閲.鐩哥瓑鍚戦噺锛氶暱搴︾浉绛変笖鏂瑰悜鐩稿悓鐨勫悜閲 &鍚戦噺鐨勮繍绠 鍔犳硶杩愮畻 AB+BC=AC锛岃繖绉嶈绠楁硶鍒欏彨鍋氬悜閲忓姞娉曠殑涓夎褰㈡硶鍒欍傚凡鐭ヤ袱...
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 ...
绛旓細鈥骞抽潰鍚戦噺鈥濇槸楂樹腑鏁板鐭ヨ瘑浣撶郴鐨勯噸瑕佺粍鎴愰儴鍒,楂樿冮鍨嬩富瑕佹湁閫夋嫨棰樸佸～绌洪锛屼篃鍙互涓庡叾浠栫煡璇嗙浉缁撳悎鍦ㄨВ绛旈涓嚭鐜帮紝骞抽潰鍚戦噺鍦ㄥ煿鍏诲鐢熻壇濂藉涔犵礌鍏汇佹彁鍗囧涔犺В棰樿兘鍔涗腑鍙戞尌鐫閲嶈浣滅敤銆傛帉鎻＄伒娲汇佸鏍枫佸疄鐢ㄧ殑瑙ｉ鏂规硶鍜岀瓥鐣ユ槸瀛﹀ソ骞抽潰鍚戦噺鐭ヨ瘑鐨勯噸瑕佹潯浠跺拰鍩烘湰瑕佷箟銆備緥涓惧洓涓柟娉曡В鍐冲钩闈㈠悜閲忛棶棰樸1 鏁...
绛旓細浜屻 鎻愬嚭璇鹃锛骞抽潰鍚戦噺 1. 鎰忎箟锛氭棦鏈夊ぇ灏忓張鏈夋柟鍚戠殑閲忓彨鍚戦噺銆備緥锛氬姏銆侀熷害銆佸姞閫熷害銆佸啿閲忕瓑 娉ㄦ剰锛1?鏁伴噺涓庡悜閲忕殑鍖哄埆锛氭暟閲忓彧鏈夊ぇ灏忥紝鏄竴涓唬鏁伴噺锛屽彲浠ヨ繘琛屼唬鏁拌繍绠椼佹瘮杈冨ぇ灏;鍚戦噺鏈夋柟鍚戯紝澶у皬锛屽弻閲嶆э紝涓嶈兘姣旇緝澶у皬銆2?浠19涓栫邯鏈埌20涓栫邯鍒濓紝鍚戦噺灏辨垚涓轰竴濂椾紭鑹氭х殑鏁板浣撶郴锛岀敤浠...
