Applications of Determinants, Condition for Collinear Points,

Applications of Determinants, Condition for Collinear Points,

Consider three-point with vertices 

 and .

if the determinant is zero when the points are collinear! 

Example 1: 

To check if the points  

 are collinear. 

Solution: 

Calculate the determinant:

 

 collinear.

Example 2) 

  For what real values ​​of the parameter 

points,  ,  and 

  are collinear? 

Solution: 

Points  

 are collinear