Show that the point A (1,-1,3), B ( 2,-4,5) and C ( 5,-13,11) are collinear.

Show that the point A (1,-1,3), B ( 2,-4,5) and C ( 5,-13,11) are coll

1.	Show that the point A (1,-1,3), B ( 2,-4,5) and C ( 5,-13,11) are collinear.
Answer» Given points , A (1,-1,3), B ( 2,-4,5) and C ( 5,-13,11) `AB= sqrt((1-2)^(2)+(-1+4)^(2)+(3-5)^(2))` `sqrt(1+9+4)=sqrt14` `BC=sqrt((2-5)^(2)+(-4+13)^2+(5+11)^2)` `sqrt(9+81+36)=sqrt126` `AC= sqrt((1-5)^(2)+(-1+13)^(2)+(3-11)^(2))` ` sqrt(16+144+64)=sqrt224` AB + BC+AC `sqrt14+sqrt126=sqrt224` `sqrt14+3sqrt14=4sqrt14` ltbr. So, the points A,B, and C are collinear.

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