Vectors

[Victoria124]

Let ABC be a triangle.Determine the position of the point M so as to :3AM-2MB+MC=0,where AM,MB,MC,0 are vectors.	​

 

[Ishuda]

Let ABC be a triangle.Determine the position of the point M so as to :3AM-2MB+MC=0,where AM,MB,MC,0 are vectors.

Do you mean these to be directed vectors? That is, for example, the vector from point M to point B (vector MB) is the 'negative of' the vector from point B to point M (vector BM)?

 

[Victoria124]

Yes

 

[HallsofIvy]

Since we are given only "a" triangle, I would do this:
Define a coordinate system with A at its origin and the positive x-axis from A through B so that B is at (a, 0). C will be at some point (b, c).
M has coordinates (x, y). Now, construct vectors AM, MB, and MC in this coordinate system to see what conditions x and y must satisfy in order that 3AM-2MB+MC=0.