◇公式の要約◇
2点 A( →a ) , B( →b ) を結ぶベクトル →AB は,→AB
=
→b −→a
![]() ○補足説明 記号 A( →a ) は,関数の記号 f(x) とは無関係。 平面の座標を表わすときに,「点 A,その座標を (3 , 4) とおく」というのを A(3 , 4) と書くのと同様にして, 「点A,その位置ベクトルを →a とおく」というのを単に,点 A( →a ) と書く。 ![]() 【注意】 →AB = →a −→b ではない! |
2点 A( →a ) , B( →b ) の中点 M の位置ベクトル →m は,
→m = ![]() ○補足説明 ![]() |
2点 A( →a ) , B( →b ) を結ぶ線分 AB m : n に内分する点 P の位置ベクトル →p は,
→p = ![]() ○補足説明 ![]() |
△ABC の頂点 A,B,C の位置ベクトルを各々 →a ,→b ,→c とすると,△ABC の重心 G の位置ベクトルは,
→g = ![]() ○補足説明 ![]() |
■ 問題 次の空欄を埋めなさい。 (半角数字[1バイト文字]で答えてください)
(1) △ABC の線分 AB,BC,CA の中点を各々 L,M,N とする。△ABC の重心 G と△LMN の重心 G ’ は一致することを証明しなさい。
|
(証明) |
(2) △ABC 頂点 A,B,C の位置ベクトルを各々 →a , →b , →c
とするとき,右の空欄を埋めなさい。
|
(3) △ABC と点 P について
→PA+2→PB+3→PC=2→AB が成り立っているとき,点 P はどのような点か。 |
(4) △ABCと点 P について
2→PA+ 3→PB+ 4→PC= →0 が成り立っているとき,点 P はどのような点か。 |
![]() ![]() |
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|