The edges of a parallelopied are of unit length and are parallel to non-coplanar unit vectors a¯,b¯,c¯ such that a¯b¯=b¯·c¯=c¯·a¯=12 . Then the volume of the parallelopiped is

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12 cu units

122 cu units

32 cu units

13 cu units

answer is A.

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Detailed Solution

a¯ b¯ c¯2=a¯.a¯a¯.b¯a¯.c¯b¯.a¯b¯.b¯b¯,c¯c¯.a¯c¯.b¯c¯.c¯= 112121211212121=12 Volume of parallel piped =[a¯b¯c¯]=12

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