两向量之纯量积.PDF

2-3铳稿悜铳句箣绱旓ゾ绌 铳稿悜铳剧殑涔樼鏈夛ジ鍊嬪畾缇╋紝涓€璎備箣绱旓ゾ 绌嶅張绋遍粸绌嶅強鍏х銆傚彟涓€璎備箣鍚戯ゾ绌嶅張 绋卞弶 绌嶅強澶栫銆傚墠鑰呮墍寰椾箣绌嶇偤绱旓ゾ锛 寰岃€呯偤 涓€鍚戯ゾ銆 鍏╁悜閲廇 鑸嘊 绱旈噺绌嶅鎴怉 锛嶣;绲愭灉瀹氱京鐐轰竴绱旈噺 锛屽ぇ灏忕瓑 鏂煎叐鍚戦噺澶у皬 锔盇 锔憋紝锔盉 锔辫垏鍚戦噺澶捐椁樺鸡涔嬮€ｇ簩涔樼锛 鍗矨 锛嶣= 锔盇 锔 锔盉 锔别€€滒€€€€€媺= AB饊€滒€€€€€媺 鍏朵腑胃鐐篈 锛孊 鍏╁悜閲忕殑澶捐 锛屼笖0 鈮 胃 鈮は€ 鍏╁悜閲忕殑绱旈噺绌岮 锛嶣= ABcos胃 锛屽湪骞句綍涓婄殑鎰忕京鐐国鍚戦噺A 涔嬪ぇ灏忓湪B 鏂瑰悜鐨勬姇褰盇cos胃涔樹互B 涔嬪ぇ灏廈 鍗矪(Acos胃) 锛 鎴栦互鍚戦噺B 涔嬪ぇ灏忓湪A 涓婄殑鎶曞奖Bcos胃 锛屼箻浠 涔嬪ぇ灏廇 鍗筹紝A (Bcos胃) 锛屽洜鑰屽緱鍒 瑙€蹇佃◣璜 鐢辩磾閲忕鐨勫畾缇╁強涓婇潰鏁樿堪锛屽彲寰椾笅鍒楄嫢骞茶蹇代 1. 鍏╁悜閲忕磾閲忕 锛屽叾绲愭灉鐐虹磾閲廂鍙互鐢ㄤ締鎺屾彙鎶曞奖閲 锛岄暦搴 鑸囪搴︾瓑骞句綍閲 2. 鍏╅潪闆跺悜閲忚嫢鏄簰鐩稿瀭鐩碅鈯(胃 = 90掳) 锛屽墖鍏剁磾閲忕鐐洪浂 锛 鍗矨 锛嶣 = 0 銆傚叐鍚戦噺鍚屽悜(胃 = 0掳) 锛孉 锛嶣= AB 銆傚叐鍚戦噺鍙嶅悜 (胃 = 180掳) 锛屽墖A 锛嶣= 锛 AB 銆備竴鍚戦噺鏈韩绱旈噺绌嶇偤鍏堕暦搴 骞虫柟 锛屽嵆A 锛嶢=A2 銆 3. 鍏╁悜閲忎箣绱旈噺绌嶇偤闆舵檪锛屽叾澶捐鍙笉蹇呯偤鐩磋銆傜敱瀹氱京鐭 锛 蟺 鐣禔=0 鎴朆=0 鎴栁 = 鏅傦紝鍧囦娇鐢ˋ 锛嶣 = 0 锛屾墍浠ュ繀闋堝湪A鈮 2 0涓擝鈮 0 锛孉 锛嶣= 0 鏅 锛屾墠鑳借A鈯(A 鍨傜洿B) 銆 4. 鍦ㄧ洿瑙掑潗妯欑郴涓 锛寈 锛寉 鍙妟 杌镐箣鍠綅鍚戦噺鍧囦簰鐩稿瀭鐩 锛岀敱 绱旈噺绌嶅畾缇 锛屽緱涓嬪垪绲愭灉 i 锛巌=1 锛宨 锛巎=0 锛宨 锛巏=0 j 锛巎=1 锛宩 锛巏=0 锛宩 锛巌=0 k 锛巏=1 锛宬 锛巌=0 锛宬 锛巎=0 5. 绱旈噺绌嶄箣閬嬬畻绗﹀悎涓嬪垪闂滀總 浜ゆ彌寰婣 锛嶣 = B 锛嶢 鍒嗛厤寰婣 锛?B+C) = A 锛嶣+A 锛嶤 绲愬悎寰媘A 锛巒B=mn(A 锛嶣)m 锛宯 鐐哄父鏁 娉ㄦ剰浜ゆ彌寰嬪拰绲愬悎寰嬪彲鐢辩磾閲忕瀹氱京鎴?2-30)寮忕煡鍏舵垚绔嬨€ 6. 鑻ュ皣鍚戦噺浠ョ洿瑙掑骇妯欑郴涔嬪垎閲忚〃绀 锛屽嵆 A=A i+A j+A k 锛孊=B i+B j+B k x y z x y z A 锛嶣 = A B +A B +A B x x y y z z 鍒版鎴戝€戝彲鐭ョ磾閲忕涔嬪€兼湁鍏╃ó姹傛硶 锛岃嫢鍏╁悜閲忓ぇ灏忓強澶捐 宸茬煡 锛岀敤(2-29)鏄彲姹傚叾鍊畸鑻ュ叐鍚戦噺鐢ㄧ洿瑙掑潗妯欏彲琛ㄧず 锛屽墖 (2-35)寮忓彲姹傚叾鍊笺€ 2-4 铳稿悜铳句箣鍚戯ゾ绌 鍏╁悜閲廇 鑸嘊 涔嬪悜閲忕锛屽彲瀹氱京涓€鍚戦噺C 锛屽鍦?-25(a)鎵€绀 锛 鍗矯=A脳B 鍚戦噺C 涔嬪ぇ灏 锔盋 锔褒 锔盇 脳B 锔褒AB sin胃 鍏朵腑胃鐐篈 鑸嘊 鍏╁悜閲忚純灏忕殑澶捐 锛屾晠sin胃鎭嗙偤姝ｅ€笺€傚悜閲廋 涔嬫柟鍚戣垏鍖呭惈A 锛孊 鍏╁悜閲忎箣骞抽潰鍨傜洿锛屼笖鎸囧悜绗﹀悎鍙虫墜瀹氬墖 锛 濡傚湒2-25 鎵€绀 锛屽嵆鎻＄穵鍙虫墜灏囨媷鎸囦几闀 锛屽洓鎸囨柟鍚戣〃绀虹敱A 杞夎嚦B 锛屾媷鎸囩殑鎸囧悜鍗崇偤鍚戦噺C 涔嬫柟鍚戙€ 鐢变笂杩扮殑瀹氱京锛屽叐鍚戦噺鐨勫悜閲忕C 锛屽彲浠ヤ互涓嬪垪寮忚〃涔 C=A 脳B=(AB sin胃)uc 鍏朵腑AB sin胃鐐篊 涔嬪ぇ灏忥紝鑰寀 鐐篊 涔嬪柈浣嶅悜閲?鍦?-25(b)) 銆 c 鐗瑰垾娉ㄦ剰鍚戦噺绌嶇殑瀹氱京鐐轰竴瑾樺皫瀹氱京 锛屽洜鍏堕