The points (4,-2,3), (5,1,2) and (7,7,0) lie on a straight line. State true or false.

True

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False

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Solution

The correct option is A
True

Let A=(4,-2,3), B=(5,1,2) and C=(7,7,0).
$A B = \sqrt{(5 - 4)^{2} + (1 - (- 2))^{2} + (2 - 3)^{2}} = \sqrt{1^{2} + 3^{2} + 1^{2}} = \sqrt{11}$
$B C = \sqrt{(7 - 5)^{2} + (7 - 1)^{2} + (0 - 2)^{2}} = \sqrt{2^{2} + 6^{2} + 2^{2}} = \sqrt{44} = 2 \sqrt{11}$
$A C = \sqrt{(7 - 4)^{2} + (7 - (- 2))^{2} + (0 - 3)^{2}} = \sqrt{3^{2} + 9^{2} + 3^{2}} = \sqrt{99} = 3 \sqrt{11}$

AC=AB+BC. Hence, A, B and C are collinear. The statement is true.

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