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

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

Answers (1)

Given points:

4(1,-1,3), 6(2,-4,5), C(5,-13,11)

Thus,

AB=\sqrt{(1-2)^{2}+(-1+4)^{2}+(3-5)^{2}}

                =\sqrt{1+9+4}=\sqrt{14}

BC=\sqrt{(2-5)^{2}+(-4+13)^{2}+(5-11)^{2}}=3\sqrt{14}

AC=\sqrt{(1-5)^{2}+(-1+13)^{2}+(3-11)^{2}}=4\sqrt{14}

Now,

AB + BC =  =\sqrt{14}+3\sqrt{14}

                  = 4\sqrt{14} = AC

Posted by

infoexpert22

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