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Prove that [vecaxxvecbvecbxxveccveccxxve...

Prove that `[vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2`

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`[vecaxxvecbvecbxxveccveccxxveca] = (vecaxxvecb).[vecbxxvec)xx(veccxxveca)]`
[using vector triple product.
=`(vecaxxvecb).{(vecbxxvecc)xxveca)vecc-(vecbxxvecc).vecc)veca}`
= `(vecaxxvecb).{((vecbxxvecc).veca)vecc} [because (vecbxxvecc).vecc = 0]`
=`{vecaxxvecb).vecc} {vecbxxvecc).veca}`
=`{veca.(vecbxxvecc} {veca.(vecbxxvecc)}`
[therefore In scalar triple product dot and cross can be interchanged and dot product is commutative.]
=`{vecavecbvec][vecavecbvecc] = [vecavecbvecc]^2` (Proved).
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MBD PUBLICATION-VECTORS-QUESTION BANK
  1. If veca, vecb and vecc mutually perpendiculars, show that [veca.(vecbx...

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  2. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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  3. Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2

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  4. For veca = hati+hatj, vecb = -hati+2hatk, vecc = hatj+hatk, obtain vec...

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  5. Prove that vecaxx(vecbxxvecc)+ vecbxx(veccxxveca)+veccxx(vecaxxvecb) =...

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  6. If veca, vecb, vecc be unit vectors and vecaxx(vecbxxvecc) = 1/2hatb, ...

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  7. Prove that the sum of the vectors directed from the vertices to the mi...

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  8. Prove by vector method that the diagonals of a quadrilateral bisect ea...

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  9. If G is the centroid of a triangle ABC, prove that vec(GA)+vec(GB)+vec...

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  10. If M is the midpoint of the side vec(BC) of a triangle ABC, prove that...

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  11. If veca and vecb are unit vectors represented by the adjacent sides of...

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  12. If the points with position vectors 10hati+3hatj, 12hati-5hatj and aha...

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  13. Prove that the four points with position vectors 2veca+3vecb-vecc, vec...

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  14. For any vector vecr = xhati+yhatj+zhatk, prove that vecr = (vecr.hati)...

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  15. If two vectors veca and vecb are such that |veca| = 3, |vecb| = 2 and ...

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  16. If veca makes equal angles with hati, hatj and hatk and has magnitude ...

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  17. If veca,vecb,vecc are such that veca.vecb = veca.vecc then show that v...

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  18. If veca+vecb+vecc = vec0, |veca| = 3 , |vecb| = 5 and |vecc| = 7, find...

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  19. If veca,vecb,vecc are unit vectors such that veca+vecb+vecc = vec0, fi...

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  20. Find the angles which the vector veca = hati-hatj+sqrt2 hatk makes wit...

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