在△ABO中向量OA=向量a,向量OB=向量b,M是OB的中点,N是AB的中点,P是ON,AM的中点,则向量AP等于多少?选项:A 2/3向量a-1/3向量b B -2/3向量a+1/3向量bC 1/3向量a-2/3向量bD -1/3向量a+2/3向量b1L的大侠,AP=(1/3)(OB-OA+
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/11 05:58:10
![在△ABO中向量OA=向量a,向量OB=向量b,M是OB的中点,N是AB的中点,P是ON,AM的中点,则向量AP等于多少?选项:A 2/3向量a-1/3向量b B -2/3向量a+1/3向量bC 1/3向量a-2/3向量bD -1/3向量a+2/3向量b1L的大侠,AP=(1/3)(OB-OA+](/uploads/image/z/11489356-28-6.jpg?t=%E5%9C%A8%E2%96%B3ABO%E4%B8%AD%E5%90%91%E9%87%8FOA%3D%E5%90%91%E9%87%8Fa%2C%E5%90%91%E9%87%8FOB%3D%E5%90%91%E9%87%8Fb%2CM%E6%98%AFOB%E7%9A%84%E4%B8%AD%E7%82%B9%2CN%E6%98%AFAB%E7%9A%84%E4%B8%AD%E7%82%B9%2CP%E6%98%AFON%2CAM%E7%9A%84%E4%B8%AD%E7%82%B9%2C%E5%88%99%E5%90%91%E9%87%8FAP%E7%AD%89%E4%BA%8E%E5%A4%9A%E5%B0%91%3F%E9%80%89%E9%A1%B9%3AA+2%2F3%E5%90%91%E9%87%8Fa-1%2F3%E5%90%91%E9%87%8Fb+B+-2%2F3%E5%90%91%E9%87%8Fa%2B1%2F3%E5%90%91%E9%87%8FbC+1%2F3%E5%90%91%E9%87%8Fa-2%2F3%E5%90%91%E9%87%8FbD+-1%2F3%E5%90%91%E9%87%8Fa%2B2%2F3%E5%90%91%E9%87%8Fb1L%E7%9A%84%E5%A4%A7%E4%BE%A0%2CAP%3D%281%2F3%29%28OB-OA%2B)
xRN@~iئLգe
/P(x1
h@w1J^=xfYZf+`B)kwZ%O:=S{Xߕ/O`=boCk.W `ˋDC- N5hm!/?_Nrz>k7ffPW
Q4l[Ť$M[
在△ABO中向量OA=向量a,向量OB=向量b,M是OB的中点,N是AB的中点,P是ON,AM的中点,则向量AP等于多少?选项:A 2/3向量a-1/3向量b B -2/3向量a+1/3向量bC 1/3向量a-2/3向量bD -1/3向量a+2/3向量b1L的大侠,AP=(1/3)(OB-OA+
在△ABO中向量OA=向量a,向量OB=向量b,M是OB的中点,N是AB的中点,P是ON,AM的中点,则向量AP等于多少?
选项:
A 2/3向量a-1/3向量b
B -2/3向量a+1/3向量b
C 1/3向量a-2/3向量b
D -1/3向量a+2/3向量b
1L的大侠,AP=(1/3)(OB-OA+AO),AO=-OA 为什么要加AO呢?
在△ABO中向量OA=向量a,向量OB=向量b,M是OB的中点,N是AB的中点,P是ON,AM的中点,则向量AP等于多少?选项:A 2/3向量a-1/3向量b B -2/3向量a+1/3向量bC 1/3向量a-2/3向量bD -1/3向量a+2/3向量b1L的大侠,AP=(1/3)(OB-OA+
选B
P点是三角形ABO的重心,所以有AP=(2/3)AM
AM=(1/2)(AB+AO)
所以AP=(1/3)(AB+AO)
因为AB=OB-OA
所以AP=(1/3)(OB-OA+AO),AO=-OA
最后得AP=(1/3)(OB-2OA)=(1/3)(b-2a)
以上的量均为向量表示