평면벡터의 투영

평면벡터의 투영
[size=150]영벡터가 아닌 두 평면벡터 [math]\large \overrightarrow{a},\, \overrightarrow{b}[/math]에 대하여 [math]\large \overrightarrow{a}=\overrightarrow{\mathrm{OA}}, \,\overrightarrow{a}=\overrightarrow{\mathrm{OB}}[/math]이고, 점 [math]\large \mathrm{B}[/math]에서 직선 [math]\large \mathrm{OB}[/math]에 내린 수선의 발을 [math]\large \mathrm{H}[/math]라 할 때, 벡터 [math]\large \overrightarrow{\mathrm{OH}}[/math]를 [math]\large \overrightarrow{a}, \,\overrightarrow{b}[/math]와 내적만을 이용하여 나타내어보자.[br][/size][br][br][center][img]data:image/png;base64,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[/img][br][/center]
[size=150]세 점 [math]\large \mathrm{B},\,\mathrm{O},\,\mathrm{H}[/math]는 한 직선 위에 있으므로 두 벡터 [math]\large \overrightarrow{\mathrm{OB}},\,\overrightarrow{\mathrm{OH}}[/math]는 서로 평행하다. 즉, 적당한 실수 [math]\large k[/math]에 대하여[br]  [math]\large \overrightarrow{\mathrm{OH}}=k\overrightarrow{\mathrm{OB}}=k\overrightarrow{b}[/math][br]이다. 두 벡터 [math]\large \overrightarrow{\mathrm{HA}},\,\overrightarrow{\mathrm{OB}} [/math]는 서로 수직이므로[br]  [math]\large \overrightarrow{\mathrm{HA}}\cdot\overrightarrow{\mathrm{OB}}=0 [/math][br]  [math]\large \left(\overrightarrow{\mathrm{OA}}-\overrightarrow{\mathrm{OH}}\right)\cdot\overrightarrow{\mathrm{OB}}=0[/math][br]  [math]\large \left(\overrightarrow{a}-k\overrightarrow{b}\right)\cdot\overrightarrow{b}=0[/math][br]  [math]\large \overrightarrow{a}\cdot\overrightarrow{b}- k \overrightarrow{b}\cdot\overrightarrow{b}=0 [/math][br]  [math]\large k \overrightarrow{b}\cdot\overrightarrow{b}=\overrightarrow{a}\cdot\overrightarrow{b}[/math][br]  [math]\large k = \frac{\overrightarrow{a}\cdot\overrightarrow{b}}{\overrightarrow{b}\cdot\overrightarrow{b}}=\frac{\overrightarrow{a}\cdot\overrightarrow{b}}{|\overrightarrow{b}|^2}[/math][br]그러므로 벡터 [math]\large \overrightarrow{\mathrm{OH}}[/math]는[br]  [math]\large \overrightarrow{\mathrm{OH}}=\frac{\overrightarrow{a}\cdot\overrightarrow{b}}{\overrightarrow{b}\cdot\overrightarrow{b}}\overrightarrow{b}[/math][br]로 나타낼 수 있다.[br][/size]
문제해결(개별)
도전 문제(개별 또는 모둠)
[size=150][b]좌표평면 위의 점 [math]\large \mathrm{A}(-1,\,3)[/math]에서 두 점 [math]\large \mathrm{B}(-2,\,-5),\, \mathrm{C}(4,\,-1) [/math]을 지나는 직선 [math]\large\mathrm{AB} [/math]에 내린 수선의 발 [math]\large \mathrm{H}[/math]의 좌표를 평면벡터 내적을 이용하여 구해보세요.[/b][/size]
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Information: 평면벡터의 투영