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if vector A B C are the three non coplanar show that vector A.(vector B × vector C)= vector B (vector C × vector A)= vector C (vector A× vector A) and it is equal to the volume of that parellelopered whose edges are along the vector A B C

if vector A B C are the three non coplanar show that vector A.(vector B × vector C)= vector B (vector C × vector A)= vector C (vector A× vector A) and it is equal to the volume of that parellelopered whose edges are along the vector A B C

Grade:12th pass

1 Answers

Deepak Kumar Shringi
askIITians Faculty 4405 Points
3 years ago
area of base of parallelepiped (parallelogram) =bxc

the vectorbxcwill be perpendicular to base

therefore the volume of parallelopiped =area of base xheight = (bxc) xAcosθ =a.(bxc)

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