Question

show that the points (1,-1,3) ,(2,-4,5)and (5,-13,11) are collinear

Answer 1

the condition for three points to be collinear is 

X1(y2z3-z2y3)-y1(x2z3-x3z2)+z1(x2z3-z2x3)=0

[1(-4(11)-(5)(-13)]-(-1)[2(11)-5(5)]+3[2(-13)-5(-4)=0

21-3-18=0

0=0

So these three points are collinear