Coordinates of three points $A, B$ and $C$ are $(3, 0, 4), (- 2, - 2, 4)$ and $(8, 2, 4)$ respectively. Show that the points $A, B$ and $C$ are collinear.

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Solution

$A B = \sqrt{(5)^{2} + (2)^{2} + (0)^{2}} = \sqrt{29}$
$B C = \sqrt{(- 10)^{2} + (- 4)^{2} + (0)^{2}} = \sqrt{116}$
$C A = \sqrt{(5)^{2} + (2)^{2} + (0)^{2}} = \sqrt{29}$
Since $C A + A B = B C$
Hence, these points are collinear.

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AB=√(5)2+(2)2+(0)2=√29BC=√(−10)2+(−4)2+(0)2=√116CA=√(5)2+(2)2+(0)2=√29Since CA+AB=BCHence, these points are collinear.

Coordinates of three points $A, B$ and $C$ are $(3, 0, 4), (- 2, - 2, 4)$ and $(8, 2, 4)$ respectively. Show that the points $A, B$ and $C$ are collinear.

$A B = \sqrt{(5)^{2} + (2)^{2} + (0)^{2}} = \sqrt{29}$
$B C = \sqrt{(- 10)^{2} + (- 4)^{2} + (0)^{2}} = \sqrt{116}$
$C A = \sqrt{(5)^{2} + (2)^{2} + (0)^{2}} = \sqrt{29}$
Since $C A + A B = B C$
Hence, these points are collinear.