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Question

The volume of the tetrahedron formed by the coterminus edges a,b and c is 3, then the volume of the parallelopiped formed by the coterminus edges a+b,b+c and c+a is

A
6
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B
18
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C
36
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D
9
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Solution

The correct option is A 36
16[¯¯¯a¯¯b¯¯c]=3
[abc]=18
Volume of the required parallelopiped
V=[a+bb+cc+a]
V=(a+b).(b+c)×(c+a)
V=2[abc]=36

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