在直角坐标平面上,一直O为原点,向量OA=(2,-4),向量OB=(-2,2),若(x乘以向量OA)+(y乘以向量OB)=3向量AB,则x=__________,y=_____________
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/29 19:17:35
![在直角坐标平面上,一直O为原点,向量OA=(2,-4),向量OB=(-2,2),若(x乘以向量OA)+(y乘以向量OB)=3向量AB,则x=__________,y=_____________](/uploads/image/z/2474755-43-5.jpg?t=%E5%9C%A8%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E5%B9%B3%E9%9D%A2%E4%B8%8A%2C%E4%B8%80%E7%9B%B4O%E4%B8%BA%E5%8E%9F%E7%82%B9%2C%E5%90%91%E9%87%8FOA%3D%EF%BC%882%2C-4%EF%BC%89%2C%E5%90%91%E9%87%8FOB%3D%EF%BC%88-2%2C2%EF%BC%89%2C%E8%8B%A5%EF%BC%88x%E4%B9%98%E4%BB%A5%E5%90%91%E9%87%8FOA%EF%BC%89%2B%EF%BC%88y%E4%B9%98%E4%BB%A5%E5%90%91%E9%87%8FOB%EF%BC%89%3D3%E5%90%91%E9%87%8FAB%2C%E5%88%99x%3D__________%2Cy%3D_____________)
在直角坐标平面上,一直O为原点,向量OA=(2,-4),向量OB=(-2,2),若(x乘以向量OA)+(y乘以向量OB)=3向量AB,则x=__________,y=_____________
在直角坐标平面上,一直O为原点,向量OA=(2,-4),向量OB=(-2,2),若(x乘以向量OA)+(y乘以向量OB)=3向量AB,则x=__________,y=_____________
在直角坐标平面上,一直O为原点,向量OA=(2,-4),向量OB=(-2,2),若(x乘以向量OA)+(y乘以向量OB)=3向量AB,则x=__________,y=_____________
AB=0B-OA=(-2-2,2+4)=(-4,6)
∵X*OA+Y*OB=3AB
∴X(2,-4)+Y(-2,2)=3(-4,6)
(2X,-4X)+(-2Y,2Y)=(-12,18)
(2X-2Y,-4X+2Y)=(-12,18)
2X-2Y=-12;-4X+2Y=18
∴X=-3;Y=3