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Prove that [vecaxxvecb,vecbxxvecc,veccxx...

Prove that `[vecaxxvecb,vecbxxvecc,veccxxveca]=[veca,vecb,vecc]^(2)`

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Prove that [veca-vecb,vecb-vecc,vecc-veca]=0

Prove that [veca+vecb vecb+vecc vecc+veca]=2[veca vecb vecc]

If veca,vecb, vecc and veca',vecb',vecc' are reciprocal system of vectors, then prove that veca'xxvecb'+vecb'xxvecc'+vecc'xxveca'=(veca+vecb+vecc)/([vecavecbvecc])

Prove that veca\'xxvecb\'+vecb\'xxvecc\'+vecc\'xxveca\'=(veca+vecb+vecc)/([veca vecb vecc])

For any four vectors veca , vecb , vecc , vecd we have (vecaxxvecb)xx(veccxxvecd)=[veca,vecb,vecd]vecc-[veca,vecb,vecc]vecd=[veca,vecc,vecd]vecb-[vecb,vecc,vecd]veca .

veca , vecb and vecc are three non-coplanar vectors and vecr . Is any arbitrary vector. Prove that [vecbvecc vecr]veca+[vecc veca vecr]vecb+[vecavecbvecr]vecc=[veca vecb vecc]vecr .

Prove that (veca.(vecbxxvecc))veca=(vecaxxvecb)xx(vecaxxvecc) .

The vectors veca-vecb,vecb-vecc,vecc-veca are

SURA PUBLICATION-MODAL QUESTION PAPER-PART - III
  1. Find the inverse of the non-singular matrix A = [[0,5],[-1,6]], by Gau...

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  2. In a competitive examination, one mark is awarded for every correct an...

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  3. State triangle inequality.

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  4. Find the condition that the roots of ax^(3)+bx^(2)+cx+d=0 are in geome...

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  5. Find the domain of sin^(-1)(2-3x^(2)).

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  6. Find the equation of the parabola with vertex (-1, -2), axis parallel ...

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  7. if the normal at the point t(1) on the parabola y^(2) = 4ax meets ...

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  8. If hat(a),hat(b),hat(c) are three unit vectors such that hat(b)andhat(...

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  9. Determine whether the pair of straight lines vecr=(2hati+6hatj+3hatk...

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  10. Prove that tan(pi/4+1/2cos^(-1)(a/b))+tan(pi/4-1/2cos^(-1)(a/b))=(2b)/...

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  11. If F (alpha)= [{:(cosalpha,0, sinalpha),(0,1,0),(-sinalpha,0,cosalpha)...

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  12. Find the values of the real numbers x and y, if the complex numbers ...

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  13. Find a polynomial equation of minimum degree with rational coefficient...

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  14. Solve : tan^(-1)((x-1)/(x-2))+tan^(-1)((x+1)/(x+2))=(pi)/(4)

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  15. The parabolic communication antenna has a focus at 2 m distance from t...

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  16. Prove that [vecaxxvecb,vecbxxvecc,veccxxveca]=[veca,vecb,vecc]^(2)

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  17. Evaluate lim(xto0^(+))(1/x-1/(e^(x)-1)).

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  18. Evaluate int(-1)^(1)log((3-x)/(3+x))dx.

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  19. From the differential equations by eliminating arbitrary constants giv...

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  20. Draw the Geometrical diagram for the sum of two complex numbers, z(1)a...

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