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Show that [veca+vecbvecb+veccvecc+veca] ...

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

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Prove that [vecaxxvecbvecbxxveccveccxxveca] = [vecavecbvecc]^2

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

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

Show that (veca-vecb)xx(veca+vecb) = 2(vecaxxvecb) . Interpret this result geometrically.

For veca = hati+hatj, vecb = -hati+2hatk, vecc = hatj+hatk , obtain vecaxx(vecbxxvecc) and also verify the formula vecaxx(vecbxxvecc) = (veca.vecc)vecb-(veca.vecb)vecc .

If veca, vecb, vecc are mutually perpendicular vectors of equal magnitude, show that veca+vecb+vecc is equally inclined to veca.vecb.vecc .

If a and b are perpendicular vectors show that (veca+vecb)^2 = (veca-vecb)^2 . [(veca+vecb)^2 means (veca+vecb).(veca+vecb) , so does (veca-vecb)^2 .]

If veca,vecb,vecc are such that veca.vecb = veca.vecc then show that veca = vec0 or vecb = vecc or veca is perpendicular to vecb.vecc .

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

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

MBD PUBLICATION-VECTORS-QUESTION BANK
  1. Find the value of lambda so that the three vectors are co-planar. (2,-...

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  2. If veca, vecb and vecc mutually perpendiculars, show that [veca.(vecbx...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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