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Let veca,vecb and vecc be the three non-...

Let `veca,vecb` and `vecc` be the three non-coplanar vectors and `vecd` be a non zero vector which is perpendicular to `veca+vecb+vecc` and is represented as `vecd=x(vecaxxvecb)+y(vecbxxvecc)+z(veccxxveca)`. Then,

A

`x^(3)+y^(3)+z^(3)=3xyz`

B

`xy+yz+zx=0`

C

`x=y=z`

D

`x^(2)+y^(2)+z^(2)=xy+yz+zx`

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OBJECTIVE RD SHARMA-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. If veca,vecb and vecc are unit coplanar vectors, then [(2veca-3vecb,...

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  2. If [(veca,vecb,vecc)]=3, then the volume (in cubic units) of the paral...

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  3. If V is the volume of the parallelopiped having three coterminous edge...

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  4. The unit vector veca and vecb are perpendicular, and the unit vector v...

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  5. If the vector vec(AB)=-3hati+4hatk and vec(AC)=5hati-lamdahatj+4hatk ...

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  6. Let veca and vecb be two mutually perpendicular unit vectors and vecc ...

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  7. Let the position vectors of vertices A,B,C of DeltaABC be respectively...

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  8. The position vector of a point P is vecr=xhati+yhatj+zhatk where x,y,z...

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  9. veca and vecb are two unit vectors that are mutually perpendicular. A...

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  10. If the vectors 2ahati+bhatj+chatk, bhati+chatj+2ahatk and chati+2ahatj...

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  11. Let vec(alpha)=ahati+bhatj+chatk,vecb=bhati+chatj+ahatk and vec(gamma)...

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  12. Let veca,vecb,vecc be three mutually perpendicular vectors having same...

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  13. Let veca,vecb and vecc be the three non-coplanar vectors and vecd be a...

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  14. Let vecr be a unit vector satisfying vecrxxveca=vecb, where |veca|=sqr...

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  15. Let veca and vecc be unit vectors such that |vecb|=4 and vecaxxvecb=2(...

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  16. If 4veca+5vecb+9vecc=vec0 then (vecaxxvecb).{(vecbxxvecc)xx(veccxxveca...

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  17. If in a triagle ABC, vec(AB)=(vecu)/(|vecu|)-(vecv)/(|vecv|) and vecAC...

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  18. Let A(2hati+3hatj+5hatk),B(-hati+3hatj+2hatk) and C(lamdahati+5hatj+mu...

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  19. A plane is parallel to the vectors hati+hatj+hatk and 2hatk and anothe...

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  20. If A,B,C,D are four points in space, then |vec(AB)xvec(CD)+vec(BC)xxve...

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