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Question
Show that the points (2, 3, 4), (– 1, 4, 5) and (8, 1, 2) are collinear
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Solution
`vec"OA" = 2hat"i" + 3hat"j" + 4hat"k"`
`vec"OB" = -hat"i" + 4hat"j" + 5hat"k"`
`vec"OC" = 8hat"i" + hat"j" + 2hat"k"`
`vec"AB" = vec"OB" - vec"OA"`
= `-hat"i" + 4hat"j" + 5hat"k" - 2hat"i" - 3hat"j" - 4hat"k"`
= `-3hat"i" + hat"j" + hat"k"`
`vec"BC" = vec"OC" - vec"OA"`
= `8hat"i" + hat"j" + 2hat"k" - 2hat"i" - 3hat"j" - 4hat"k"`
= `6hat"i" - 2hat"j" - 2hat"k"`
= `-2(-3hat"i" + hat"j" + hat"k")`
`vec"BC" = - 2vec"AB"`
∴ Given points are collinear.
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