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The triple product of (vec d + vec a) ....

The triple product of ` (vec d + vec a) .[ vec a xx ( vec b xx ( vec c xx vec d ))]` is equal to:

Text Solution

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`(vecd+veca).[vecaxx(vecbxx(veccxxvecd))]`
`=(vecd+veca).[vecaxx((vecb.vecd)vecc-(vecb.vecc)vecd)]`
`=(vecd+veca).[(vecb.vecd)(vecaxxvecc)-(vecb.vecc)(vecaxxvecd)]`
`=(vecb.vecd)([vecd.veca.vecc + veca.veca.vecc]) - (vecb.vecc)([veca.vecd.vecd+veca.veca.vecd])`
We know, if in a scalar triple product, two same values are there, value of products is `0`.
So, our expression becomes,
`=(vecb.vecd)([vecd.veca.vecc+0])-(vecb.vecc)([0-0])`
`=(vecb.vecd)[vecd.veca.vecc]`
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