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Question
For any three vectors `veca, vecb` and `vecc`, `(veca - vecb).(vecb - vecc) xx (vecc - veca)` = ______.
Options
0
`veca.vecb xx vecc`
`2veca.vecb xx vecc`
`veca.vecc xx vecb`
MCQ
Fill in the Blanks
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Solution
For any three vectors `veca, vecb` and `vecc`, `(veca - vecb).(vecb - vecc) xx (vecc - veca)` = 0.
Explanation:
`(veca - vecb).(vecb - vecc) xx (vecc - veca)`
= `(veca - vecb).(vecb xx vecc - vecb xx veca + vecc xx veca)`
= `veca.(vecb xx vecc) - vecb.(vecc xx veca)`
= `veca.(vecb xx vecc) + vecb.(veca xx vecc)`
= `veca.(vecb xx vecc) - (veca xx vecb).vecc`
= `veca.(vecb xx vecc) - veca.(vecb xx vecc)`
= 0
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Coplanarity of Three Vectors and Four Points
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