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  • Prove that the points (0, – 1, – 7), (2, 1, – 9) and (6, 5, – 13) are collinear. Find the ratio in which the first point divides the join of the other two

Prove that the points (0, – 1, – 7), (2, 1, – 9) and (6, 5, – 13) are collinear. Find the ratio in which the first point divides the join of the other two

Answers (1)

Given:

4(0,-1,-7), 8(2,1,-9) & C(6,5,-13)

Now,

AB = \sqrt{(0-2)^{2}+(-1-1)^{2}+(-7+9)^{2} }

                  \sqrt{4+4+4}=2\sqrt{3}

BC =  \sqrt{(2-6)^{2}+(1-5)^{2}+(-9+13)^{2} }

                  \sqrt{16+16+16}=4\sqrt{3}

AC =    \sqrt{(0-6)^{2}+(-1-5)^{2}+(-7+13)^{2} }

                  \sqrt{36+36+36}=6\sqrt{3}

Now, AB + BC = 2\sqrt{3}+4\sqrt{3}

                  = 6\sqrt{3}

                  = AC

Thus, A,B & C are collinear.

AB:AC = 2\sqrt{3}:6\sqrt{3}

                  = 1:3

Thus, A divides BC externally in the ratio 1:3.

Posted by

infoexpert22

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