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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 `hat(a), hat(b), hat(c)` such that `hat(a)*hat(b)=hat(b)*hat(c)=hat(c)*hat(a)=(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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MODERN PUBLICATION-VECTORS-Exercise
  1. If (vecaxxvecb)^2+(veca*vecb)^2=144 and |veca|=4, then |vecb|=

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

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

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  4. If a, b, c and d are the unit vectors such that (atimesb)*(ctimesd)=1 ...

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  5. If vecu, vecv, vecw are non -coplanar vectors and p,q, are real numbe...

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  6. Let veca =hatj-hatk and vecc =hati-hatj-hatk. Then the vector b satisf...

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  7. If the vectors veca=hati-hatj+2hatk.vecb=2hati+4hatj+hatk and vec c=la...

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  8. The vectors veca and vecb are not perpendicular and vecc and vecd are ...

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  9. Let veca=hati+hatj+hatk, vecb=hati-hatj+hatk and vecc=hati-hatj-hatk b...

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  10. If the vectors phati+hatj+hatk,hati+qhatj+hatk and hati+hatj+rhatk(p n...

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  11. Let a,b and c be three non-zero vectors which are pairwise non-colline...

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  12. Let veca and vecb be two unit vectors. If the vectors : vecc=veca+2vec...

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  13. Let ABCD be a parallelogram such that AB=q, AD=p and angleBAD be an ac...

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  14. If veca and vecb are vectors such that |veca+vecb|=sqrt(29) and vecaxx...

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  15. If the vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj-4hatk are t...

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  16. Let vec(PR)=3hati+hatj-2hatk and vec(SQ)=hati-3hatj-4hatk determine di...

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  17. If [vecaxxvecb vecbxxvecc veccxxveca]=lambda[veca vecb vecc]^2, ...

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  18. Let veca,vecb and vecc be three non-zero vectors such that no two of t...

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  19. Let veca,vecb and vecc be three unit vectors such that : vecaxx(vecbxx...

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  20. Find the values of 'x' for which x(hati+hatj+hatk) is a unit vector.

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