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Solution - 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. - Scalar Triple Product of Vectors

Question

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.

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

 

 

 

 

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2014-2015 (March)
Question 2.1.1 | 3 marks

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Solution for question: 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. concept: Scalar Triple Product of Vectors. For the courses HSC Arts, HSC Science (Computer Science), HSC Science (Electronics), HSC Science (General)
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