HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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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. - HSC Science (Electronics) 12th Board Exam - Mathematics and Statistics

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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APPEARS IN

 2014-2015 (March) (with solutions)
Question 2.1.1 | 3 marks

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Reference Material

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 Science (Electronics), HSC Science (Computer Science), HSC Arts, HSC Science (General)
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