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If A, B, C, D Are (1, 1, 1), (2, I, 3), (3, 2, 2), (3, 3, 4) Respectively, Then Find the Volume of Parallelopiped with AB, AC and AD as the Concurrent Edges. - Mathematics and Statistics

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If A, B, C, D are (1, 1, 1), (2, I, 3), (3, 2, 2), (3, 3, 4) respectively, then find the volume of parallelopiped with AB, AC and AD as the concurrent edges.

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Solution

Given that A,B,C and D are (1, 1, 1), (2, 1, 3) , (3, 2, 2) and (3, 3, 4) respectively.
We need to find the volume of the parallelopiped with AB, AC and AD as the concurrent edges.
The volume of the parallelopiped whose coterminus edges are a, b and c is `[veca vecbvecc]=veca.(vecbxxvecc)`

Given that A,B,C and D are (1, 1, 1) , (2, 1, 3) , (3, 2, 2) and (3, 3, 4)

`vec(AB)=(2-1)hati+(1-1)hatj+(3-1)hat k`

`=hati+2hatk`

`vec(AC)=(3-1)hati+(2-1)hatj+(2-1)hat k`

`=2hati+hatj+hatk`

`vec(AD)=(3-1)hati+(3-1)hatj+(4-1)hat k`

`=2hati+2hatj+3hatk`

`[veca vecbvecc]=|[1,0,2],[2,1,1],[2,2,3]|`

                =1(3-2)-0+2(4-2)

                =1+4

                = 5 cubic units

 

 

 

 

Concept: Scalar Triple Product of Vectors
  Is there an error in this question or solution?

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