Show that the points (2,−1,3),(4,3,1) and (3,1,2) are collinear.

Engineering

Mathematics

Equation of Straight Line in 3D

theorem in space

Question

Show that the points (2,−1,3),(4,3,1) and (3,1,2) are collinear.

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X₁,Y₁,Z₁ = 2,–1,3

X₂,Y₂,Z₂ = 4,3,1

X₃, Y₃,Z₃ = 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.