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Let vec(alpha),vec(beta) and vec(gamma b...

Let `vec(alpha),vec(beta)` and `vec(gamma` be the unit vectors such that `vec(alpha)` and `vec(beta)` are mutually perpendicular and `vec(gamma)` is equally inclined to `vec(alpha)` and `vec(beta)` at an angle `theta`. If `vec(gamma)=xvec(alpha)+yvec(beta)+z(vec(alpha)xxvec(beta))`, then which one of the folllowing is incorrect?

A

`z^(2)=1-2x^(2)`

B

`z^(2)=1-2y^(2)`

C

`z^(2)=1-x^(2)-y^(2)`

D

`x^(2)+y^(2)=1`

Text Solution

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The correct Answer is:
D
NA
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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. If vecaxx(vecaxxvecb)=vecbxx(vecbxxvecc) and veca.vecb!=0, then [(veca...

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  2. [(veca,vecb,axxvecb)]+(veca.vecb)^(2)=

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  3. Let vec(alpha),vec(beta) and vec(gamma be the unit vectors such that v...

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  4. If veca, vecb and vecc are unit coplanar vectors, then [(2veca-3vecb,...

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

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  6. If V is the volume of the parallelepiped having three coterminous edge...

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  7. Unit vectors veca and vecb ar perpendicular , and unit vector vecc is ...

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  8. If vectors vec A B=-3 hat i+4 hat ka n d vec A C=5 hat i-2 hat j+4 ha...

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

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

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

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

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  13. Let alpha = a hati + b hatj + chatk , vecbeta = bhati + chatj + ahatk ...

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

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

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  16. Let vecr be a unit vector satisfying vecr xx veca = vecb, " where " |v...

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

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  18. If veca+2vecb+3vecc=0, then vecaxxvecb+vecbxxvecc+veccxxveca=

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  19. If in triangle ABC, vec(AB) = vecu/|vecu|-vecv/|vecv| and vec(AC) = (...

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  20. Let A(2hat(i)+3hat(j)+5hat(k)), B(-hat(i)+3hat(j)+2hat(k)) and C(lambd...

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