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The edges of a parallelopiped are of uni...

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors `hata, hatb, hatc` such that `hata.hatb=hatb.hatc=hatc.hata=1//2.` Then the volume of the parallelopiped is :

A

`(1)/(sqrt2)`

B

`(1)/(2sqrt2)`

C

`(sqrt3)/(2)`

D

`(1)/(sqrt3).`

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The correct Answer is:
A
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MODERN PUBLICATION-VECTOR ALGEBRA -Multiple Choice Question (Level-II)
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  3. Let veca, vecb, and vecc be three non-zero vectors such that no two of...

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  4. If veca = (hati +hat j + hatk), veca.vecb=1 and veca xx vecb=hatj-hatk...

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  5. If veca, vecb, cecc are non-coplanar vectors and lamda is a real numbe...

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  6. If hatu and hatv are unit vactors and theta is the angle between them,...

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  7. Let veca = hat i + hatj + hatk, vecb = hati + 2 hatk and vecc = x hati...

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  8. The vector veca = alpha hati + 2 hatj + beta hatk lies in the plance o...

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  9. The non-zero vectors veca, vecb and vecc are related by veca = 8 vecb ...

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  10. Let the vectors veca, vecb, vecc and vecd be such that (veca xx vecb) ...

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  11. The unit vector which is orthgonal to the vector veca=3hati+2hatj+6hat...

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  12. If veca, vecb, vecc are three non-zero, non-coplanar vectors and vec...

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  13. Let veca = hati + hatj + hatk, vecb = hati - ahtj + hatk and hati - ha...

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  14. The number of distinct real values of lamda, for which the vectors : ...

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  15. Let veca, vecb, vecc be unit vectors such that veca + vecb + vecc = v...

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  16. The edges of a parallelopiped are of unit length and are parallel to n...

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  17. Let two non-collinear unit vectors hata and hatb form an acute angle. ...

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  18. If vec u , vec nu, and vec w are non coplanar vectors and p,q are real...

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  19. If veca , vecb, vecc and vecd are unit vectors such that (veca xx vecb...

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  20. Let (P (3,2,6) be a point in space and Q be point on the line vecr = (...

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