已知P为三角形ABC内一点,且3向量AP+4向量BP+5向量CP=向量O,延长AP交BC于点D,若向量AB=向量a,向量AC=向量b,用向量a,b表示向量AP,AD
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![已知P为三角形ABC内一点,且3向量AP+4向量BP+5向量CP=向量O,延长AP交BC于点D,若向量AB=向量a,向量AC=向量b,用向量a,b表示向量AP,AD](/uploads/image/z/3471151-31-1.jpg?t=%E5%B7%B2%E7%9F%A5P%E4%B8%BA%E4%B8%89%E8%A7%92%E5%BD%A2ABC%E5%86%85%E4%B8%80%E7%82%B9%2C%E4%B8%943%E5%90%91%E9%87%8FAP%2B4%E5%90%91%E9%87%8FBP%2B5%E5%90%91%E9%87%8FCP%3D%E5%90%91%E9%87%8FO%2C%E5%BB%B6%E9%95%BFAP%E4%BA%A4BC%E4%BA%8E%E7%82%B9D%2C%E8%8B%A5%E5%90%91%E9%87%8FAB%EF%BC%9D%E5%90%91%E9%87%8Fa%2C%E5%90%91%E9%87%8FAC%EF%BC%9D%E5%90%91%E9%87%8Fb%2C%E7%94%A8%E5%90%91%E9%87%8Fa%2Cb%E8%A1%A8%E7%A4%BA%E5%90%91%E9%87%8FAP%2CAD)
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已知P为三角形ABC内一点,且3向量AP+4向量BP+5向量CP=向量O,延长AP交BC于点D,若向量AB=向量a,向量AC=向量b,用向量a,b表示向量AP,AD
已知P为三角形ABC内一点,且3向量AP+4向量BP+5向量CP=向量O,延长AP交BC于点D,若向量AB=向量a,向量AC=向量b,用向量a,b表示向量AP,AD
已知P为三角形ABC内一点,且3向量AP+4向量BP+5向量CP=向量O,延长AP交BC于点D,若向量AB=向量a,向量AC=向量b,用向量a,b表示向量AP,AD
3AP+4BP+5CP=0
即:3AP+4(AP-AB)+5(AP-AC)
=12AP-4AB-5AC=0
即:AP=4AB/12+5AC/12=(4a+5b)/12
令:AP=kPD,则:PD=(4AB+5AC)/(12k)
令:AD=xAB+yAC,则:x+y=1
则:PD=AD-AP=(x-4/12)AB+(y-5/12)AC
故:x-1/3=1/(3k),y-5/12=5/(12k)
即:(x-1/3)/(y-5/12)=4/5
即:5x=4y,即:4y/5+y=1
即:y=5/9,x=4/9
故:AD=4AB/9+5AC/9=(4a+5b)/9