मराठी

A→,B→ and C→ are three non coplanar vectors, then (A→+B→+C→).((A→+B→)×(A→+C→)) is equal to ______.

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प्रश्न

`vecA, vecB` and `vecC` are three non coplanar vectors, then `(vecA + vecB + vecC).((vecA + vecB) xx (vecA + vecC))` is equal to ______.

पर्याय

  • 0

  • `[vecA, vecB, vecC]`

  • `2[vecA, vecB, vecC]`

  • `-[vecA, vecB, vecC]`

MCQ
रिकाम्या जागा भरा
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उत्तर

`vecA, vecB` and `vecC` are three non coplanar vectors, then `(vecA + vecB + vecC).((vecA + vecB) xx (vecA + vecC))` is equal to `-[vecA, vecB, vecC]`.

Explanation:

`[(vecA + vecB + vecc, vecA + vecB, vecA + vecC)]`

= `|(1, 1, 1),(1, 1, 0),(1, 0, 1)|[vecAvecBvecC]`

= `-[vecA, vecB, vecC]`

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Coplanarity of Three Vectors and Four Points
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