Show that the points \left(\right. 2 , - 1 , 3 \left.\right) , \left(\right. 4 , 3 , 1 \left.\right) and \left(\right. 3 , 1 , 2 \left.\right) are collinear.

Engineering

Mathematics

Line of Greatest Slope

Question

Show that the points

(2, - 1, 3), (4, 3, 1)

and

(3, 1, 2)

are collinear.

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X_{1}, Y_{1}, Z_{1}

2, - 1, 3

X_{2}, Y_{2}, Z_{2}

4, 3, 1

X_{3}, Y_{3}, Z_{3}

3, 1, 2

\frac{X_{1} - X_{2}}{X_{2} - X_{3}} = \frac{Y_{1} - Y_{2}}{Y_{2} - Y_{3}} = \frac{Z_{1} - Z_{2}}{Z_{2} - Z_{3}}

\frac{- 2}{1} = \frac{- 4}{2} = \frac{2}{- 1}

\frac{- 2}{1} = \frac{- 2}{1} = \frac{- 2}{1}

Hence, the points are coplanar.

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