Tetrahedron!
Geometry
Level
4
The volume of tetrahedron whose vertices are (1,1,1), (2,3,4), (2,-1,1) and (1,-2,0) is V. Find the value of 6V.
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6
5/6
30
None of three given choices
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1 solution
Volume of the tetrahedron: 6 1 [ a , b , c ] where [ a , b , c ] denotes the scalar triple product of three vectors. For the problem: set ( 1 , 1 , 1 ) as the reference point. therefore the 3 vectors would be: V 1 : 1 i + 2 j + 3 k ; V 2 = 1 i − 2 j + 0 k ; V 3 = 0 i − 3 j − k on evaluating the expression we get volume: 6 5 hence the answer 6 units 3