Question

Check if the points $(1,2,3)(7,0,1)(-2,3,4)$ are collinear or not.

Answer 1

$A(1,2,3)B(7,0,1)C(-2,3,4)$

Dist b/w $AB=\sqrt{(7-1{)}^2+(0-2{)}^2+(1-3{)}^2}$

$=\sqrt{36+4+4}$

$=\sqrt{44}=6.63$

Dist b/w $BC=\sqrt{(7+2{)}^2+(0-3{)}^2+(1-4{)}^2}$

$=\sqrt{36+9+9}=\sqrt{54}=7.35$

Dist b/w $AC=\sqrt{(1+2{)}^2+(2-3{)}^2+(3-4{)}^2}$

$=\sqrt{9+1+1}=\sqrt{11}=3.32$

As, we can see,

$AB+AC\ne BC$

So, PCs are not collinear.