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 A36 16[¯¯¯a¯¯b¯¯c]=3 ⇒[→a→b→c]=18
Volume of the required parallelopiped V=[→a+→b→b+→c→c+→a] V=(→a+→b).(→b+→c)×(→c+→a) V=2[→a→b→c]=36