Given three points a (- 1,1,2), B (1,2, - 1), C (a, 0,3), can these three points be collinear? Given three points a (- 1,1,2), B (1,2, - 1), C (a, 0,3), can these three points be collinear? If they can be collinear, find out the value of a; if not, explain the reason,

Given three points a (- 1,1,2), B (1,2, - 1), C (a, 0,3), can these three points be collinear? Given three points a (- 1,1,2), B (1,2, - 1), C (a, 0,3), can these three points be collinear? If they can be collinear, find out the value of a; if not, explain the reason,

The method of permanent vector
Suppose three points a (- 1,1,2), B (1,2, - 1) and C (a, 0,3) can be collinear
Then the vector AB = m and the vector BC
That is ab = (2,1, - 3), BC = (A-1, - 2,4)
That is, (2,1, - 3) = m (A-1, - 2,4)
The equations are obtained
2=m（a-1）
1=-2m
-3=4m
The solution is that m does not exist, that is, a does not exist
Therefore, three points a (- 1,1,2), B (1,2, - 1), C (a, 0,3) cannot be collinear

Given a > 0, if three points a (1, - a), B (2, a & sup2;), C (3, a & sup3;) in the plane are collinear, then a is equal to 0

Formula:
[a²-（-a）]/(2-1)=[a³-a²]/(3-2)
Ask for the rest

If three points a (2,3) B (3, - 2) C (1 / 2, m) are collinear, then the value of M is

A (2,3) B (3, - 2) C (1 / 2, m) three points collinear
be
Kab=Kac
(-2-3)/(3-2)=(m-3)/(1/2-2)
-5=(m-3)/ -3/2
m-3=-5*(-3/2)=15/2
m=3+15/2=21/2

If point a (- 2, m) B (m, 4) C (- 3,1-m) is collinear, then the value of M is?

(4-m)/(m+2)=(1-2m)/-1=(3+m)/(3+m) m=1