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The edges of parallelopiped are of unit ...

The edges of parallelopiped are of unit length and are parallel to non-coplanar unit vectors `hata,hatb,hatc` such that `hata.vecb=vecb.vec cvec c.veca=(1)/(2)` then find volume of parallelopiped.

A

`1/(sqrt(2))`

B

`-1/(sqrt(2))`

C

`1/(2sqrt(2))`

D

`-1/(2sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`:.(hataxxhatb).{(hata.hatb)hatb-(hata.hatb)hatc}=0-(hata.hatb)[(hata, hatb, hatc)]`
`=-1/2xx1/(sqrt(2))`
`:.[(hata, hatb, hatc)]^(2)=|(1, 1/2, 1/2),(1/2, 1, 1/2),(1/2, 1/2, 1)|=1/2`
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