HSC Arts 12th Board ExamMaharashtra State Board
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Find the volume of tetrahedron whose coterminus edges are 7i+k; 2i+5j−3k and 4i+3j+k - HSC Arts 12th Board Exam - Mathematics and Statistics

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Question

Find the volume of tetrahedron whose coterminus edges are `7hat i+hatk; 2hati+5hatj-3hatk and 4 hat i+3hatj+hat k`

Solution

Volume of tetrahedron whose conterminus edges are `bara,barb and barc " is " 1/6[bara barb barc].`

`"Here " bara=7hati+hatk; barb=2hati+5hatj-3hatk;barc=4hati+3hatj+hatk.`

Volume of tetrahedron  `=1/6[bara,barb,barc]`

                                   `=1/6|[7,0,1],[2,5,-3],[4,3,1]|`

                                   `=1/6[7(5+9)-0(2+12)+1(6-20)]`

                                   `=1/6[98-0-14]`

                                   `=1/6[84]`

                                    = 14  

 Hence volume of tetrahedron is 14 cubic units.                           

                                    

                                   

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APPEARS IN

 2015-2016 (March) (with solutions)
Question 3.1.1 | 3.00 marks

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Solution Find the volume of tetrahedron whose coterminus edges are 7i+k; 2i+5j−3k and 4i+3j+k Concept: Three Dimensional Geometry - Problems.
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