# 3388gg.com：2018_2019高中数学第2章平面向量2.4第2课时平面向量数量积的坐标运算学案苏教版必修4201

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2 1. .2..3. ij x y 1 iijjij ii11cos01jj11cos01 ij0. 2 ij a(x1y1)b(x2y2) ab ij ab. ax1iy1jbx2iy2j ab(x1iy1j)(x2iy2j)x1x2i2(x1y2x2y1)ijy1y2j2x1x2y1y2. 3 ab ab abab0x1x2y1y20. a(x1y1)b(x2y2). abx1x2y1y2 abx1x2y1y20 1 a(xy)|a| axiyjxyR a2(xiyj)2(xi)22xyij(yj)2 x2i22xyijy2j2. i21j21ij0 a2x2y2|a|2x2y2 |a| x2y2. 2 A(x1y1)B(x2y2)AB 1 ABOBOA (x2y2)(x1y1) (x2x1y2y1) |AB| x2x12y2y12. a(xy) A(x1y1)B(x2y2)AB |a| x2y2 |AB| x2x12y2y12 ab ab a(x1y1)b(x2y2) a b cos |a||b| x21x1xy122y1yx222y22. 1 a(x1y1)b(x2y2) abx1x2y1y20.( ) 2 a(x1y1)b(x2y2) abx1y2x2y10.( ) 3 cos >0 ( ) cos 1>0 0. 1 a b b(12)ab10. (1) a (2) c(21) a(bc)(ab)c. (1) a b( 2 )( >0) ab 4 10 2a(24) (2)bc12210ab10 a(bc)0a0(ab)c10(21)(2010) 2 (ab)ca(bc) 1 a(11)b(12)(2ab)a________. 1 a(11)b(12) 2ab2(11)(12)(10)(2a b)a(10)(11)1. 2 xOy O () A(1612)B(515) (1)|OA||AB| (2)OAB. (1)OA(1612) AB(5161512)(213) |OA| 16212220|AB| 2123215 2. (2)cosOAB AOAB? AOAB |AO||AB| . AOABOAAB [16(21)123]300. cosOAB 300 2015 2 22. OAB45. (1) (2)|a| x2y2 (3) cos 2 a(11)b( 1) a b a(11)b( 1) |a| 2|b| 1 2ab 1. 3 ab 1<0 2 1 21 <1 22 10. <1 1. (1)(11) 3 (1) a(32)b(10) ab a2b ________ 17 ab a2b ( ab)(a2b)0. a(32)b(10) (3 12 )(12)0 3 14 0 17. (2)ABC AB(23)AC(1k)ABC k AB(23)AC(1k) BCACAB(1k3) A90ABAC213k0k23 B90ABBC2(1)3(k3)0 k131 C90ACBC1(1)k(k3)0 k32 13. k 2313132 13. 3 xOy A(14)B(23)C(21)(ABtOC) OC t________. 4 1 AB(31) ABtOC(32t1t) OC(21)(ABtOC)OC (32t)2(1t)(1)0. t1. 1 a(31)b(12) a b ________ 4 |a| 10|b| 5ab5. cosab|aa||bb| 5 10 5 22. ab [0 ] a b 4 . 2BA12 23BC 2312ABC________. 30 |BA|1|BC|1 cosABCB|ABA ||B CB|C 23 ABC30. 3 m( 11)n( 22)(mn)(mn) ________. 3 mn(2 33)mn(11) (mn)(mn)(mn)(mn)(2 33)(11)2 60 3. 4 ab a(43)|b|1 ab5 b____________. 4535 |a|5cosab|aa||bb|1 5 ab b15a4535. 5 a(43)b(12) (1) a b (2)(a b)(2ab) (1)ab4(1)322 |a| 42325|b| 1222 5 cosab|aa||bb|5 2 25 5 25 . (2)a b(4 32 )2ab(78)(a b)(2ab) (a b)(2ab)7(4 )8(32 )0 52 9 . 1 2 3 a(x1 y1)b(x2y2) abx1y2x2y10abx1x2y1y20. 4 1 a(12)2ab(31) ab________. 5 a(12)2ab(31) b2a(31)2(12)(31)(13) ab(12)(13)1235. 2 a(1n)b(1n) 2ab b |a|________. 2 6 (2ab)b2ab|b|2 2(1n2)(1n2)n230 n23|a| 12n22. 3 a(12)b(11) 2ab ab ________ 4 2ab2(12)(11)(33) ab(12)(11)(03) (2ab)(ab)9 |2ab|3 2|ab|3. cos 3 9 23 22 0 4 . 4 a(23) a _____________

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