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Prove that the four points with position...

Prove that the four points with position vectors `2veca+3vecb-vecc, veca-2vecb+3vecc, 3veca+4vecb-2vecc` and `veca-6vecb+6vecc` are coplanar.

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For any three vectors veca,vecb,vecc show that [(veca-vecb) (vecc-veca) (vecb-vecc)] = 0

Show that veca, vecb and vec c are coplanar if veca+vecb,vecb+vecc and vecc+veca are coplanar.

For the non-zero vectors veca, vecb and vecc, veca.(vecbxxvecc) = 0 if

|veca| = |vecb| = veca = vecb .

(-veca).vecbxx(-vecc)) =

If veca=vecb+vecc, then write the value of veca*(vecbxxvecc).

Prove that : |veca + vecb|le|veca|+|vecb| .

Show that the vector area of the triangle whosse vertices have position vector veca,vecb,vecc is 1/2(vecaxxvecb+vecbxxvecc+veccxxveca) .

If veca,vecb and vecc are three vectors such that veca x vecb = vecc and vecb x vecc = veca , then prove that veca,vecb and vecc are mutually at right angles and |vecb| = 1,|vecc| = |veca|

MBD PUBLICATION-VECTORS-QUESTION BANK
  1. Show that [veca+vecbvecb+veccvecc+veca] = 2[vecavecbvecc]

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  20. Find the angle between veca and vecb if |vecaxxvecb| = veca.vecb

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