Show that the points A(– 7, 4, – 2), B(– 2, 1, 0) and C(3,

Engineering

Mathematics

Introduction to Determinants

Question

Show that the points A(– 7, 4, – 2), B(– 2, 1, 0) and C(3, – 2, 2) are collinear.

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Given,

A(– 7, 4, – 8), B(– 2, 1, 0), C(– 3, – 2, 2)

Since, $\vec{AB} = \vec{OB} - \vec{OA}$

$\vec{AB} = (- 2 i + j + 0 k) - (- 7 i + 4 j - 2 k)$

$\vec{AB} = 5 i - 3 j + 2 k$

Since, $\vec{AC} = \vec{OC} - \vec{OA}$

$\vec{AC} = (3 i - 2 j + 2 k) - (- 7 i + 4 j - 2 k)$

$\vec{AC} = 10 i - 6 j + 4 k$

$\vec{AC} = 2 (5 i - 3 j + 2 k) = 2 \vec{AB}$

Therefore, A, B, C are collinear.

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