The edges of a parallelopiped are of unit length and are parallel to non coplanar unit vectors a^, b^,c^, such that a^.b^=b^c^=c^.a^=1/2. What is the volume of the parallelopiped?

volume of the parallelopiped is given by:-

a.(b×c)   .....(i)

going by the question these unit vectors are arranged at 60 degree andle to each other

so easily if you visualise the diagram taking b vector and c vector on 1 plane

then a vecotr will make 45 degree with the vertical!!!

so magnitude of the expression (i) is:-

1 * cos45

1/√2 suare units

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