Question

Show that the points :
(-2,3, 5), (1,2, 3), (7, 0, -1 ) are collinear

Answer 1

Formulas that to be used are :-

Ex: Prove that A(1, -1) , B(5,2) , C(9,5) are co-linear.  

Solution: Given: A(1, -1) (x1,y1)  

                            B(5,2) (x2, y2)  

                            C(9,5) (x3, y3)  

Method 1 :  

AC=AB+BC (here use distance formula, and then if it comes LHS=RHS) hence we proved

 

Method 2:

Use Area of triangle formula (here we should take LHS as '0')  

0=1/2[x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]

(Do until LHS=RHS)  

Then, hence it is proved that points are co-linear