For three vectors with a common starting point on the plane, the necessary and sufficient condition for the straight line where the ending point is located is that one vector can be expressed linearly by two of them, and the sum of the coefficients is 1.

Symbolic language: (because it is not easy to match, the vector AB is represented by "AB")

OC = M OA+N OB, then the necessary and sufficient condition for M N =1is the straight line of A, B, C, B and C.

The principle is deduced as follows:

1. Because "CE" and "CA" are parallel (that is, * * * lines), there is a basic theorem of parallel vectors, "CE" = m "CA".

2. Because "CE" = "BE"-"BC" and "CA" = "BA"-"BC", so

("be"-"BC") = m× ("ba"-"BC"), and the arrangement is m "ba"+(1-m) "BC" = "be".

3. It can be seen from the process of derivation that the sum of the coefficients of "←BA" and "←BC" is exactly 1.

In addition, we can also use "AE" = n "CA" and "CE" = k "EA" to deduce, and we can also draw a similar conclusion, but the sum of the coefficients is 1.