Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are col… - Vidyadip

Question

Show that the points (-2, 3, 5), (1, 2, 3) and (7, 0, -1) are collinear.

✓

Answer

Let A(-2, 3, 5), B (1, 2, 3) and C(7, 0, -1) be three given points.
$\begin{array}{l}
\text { Then } A B=\sqrt{(1+2)^2+(2-3)^2+(3-5)^2}=\sqrt{9+1+4}=\sqrt{14} \\
B C=\sqrt{(7-1)^2+(0-2)^2+(-1-3)^2}=\sqrt{36+4+16}=\sqrt{56}=2 \sqrt{14} \\
A C=\sqrt{(7+2)^2+(0-3)^2+(-1-5)^2}=\sqrt{81+9+36}=\sqrt{126}=3 \sqrt{14}\end{array}$
Now $AC = AB + BC$
Therefore,A,B,C are collinear.

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