高一数学平面向量基本定理

平面向量基本定理

平面向量基本定理： 如果e1,e2是同一平面内的两个不共线向量，那么对于这一平面内的任一向量a，有且只有一对实数λ1，λ2使a= λ1 e1+ λ2 e2我们把不共线的向量e1,e2叫做表示这一平面内所有向量的一组基底。

M

e1ae2O

Aa

BC

N

例题1.已知向量e1,e2，求作向量-2.5e1+3e2DCM例题2.如图平行四边形ABCD的两条对角线相交于点M，b

AB?a,AD?b，用 且 AaB

a,b表示MA，MB，MC和MD练习：已知平行四边形ABCD的两条对角线AC与BD相交于点E，O是任意一点，求证：　例题3.如图

OA,OB不共线，AP?tAB(t?R),用OA，OB表示OPDOC

AEBPBO

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