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Prove that vecaxx(vecbxxvecc)+ vecbxx(ve...

Prove that `vecaxx(vecbxxvecc)+ vecbxx(veccxxveca)+veccxx(vecaxxvecb)` = 0 and hence prove that `vecaxx(vecbxxvecc), vecbxx(veccxxveca), veccxx(vecaxxvecb)` are coplanar.

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Prove that veca xx (vecb xx vecc) + vecb xx (vecc xx veca) + vecc xx (veca xx vecb) = vec0 and hence prove that veca xx (vecb xx vecc), vecb xx (vecc xx veca), vecc xx (veca xx vecb) are coplanar.

If vecaxxvecb = vecbxxvecc ne vec0 , prove that veca+vecc = mvecb , where m is a scalar.

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

SHARAM PUBLICATION-VECTORS-EXAMPLE
  1. Find the unit vector in the direction of veca-vecb where veca= 4hati +...

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  2. If a and b are perpendicular vectors show that (veca+vecb)^2 = (veca-v...

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

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  4. If veca = 3hati+hatj-2hatk, vecb = 2hati-3hatj+4hatk then verify that ...

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

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  6. Show that veca, vecb and vec c are coplanarif veca+vecb,vecb+vecc and ...

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  7. Find the vector vecp which is perpendicular to both vecalpha = 4hati +...

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  8. If veca=hati+hatj+hatk and vecb=hati-hatk . Find a vector vecc such th...

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  9. If veca,vecb and vecc are three vectors such that |veca|=5,|vecb|=12,|...

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  10. If a=2hati+hatk,b=hati+hatj+hatkandc=4hati-3hatj+7hatk, then find the ...

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  11. Prove the following by vector method. in any triangle ABC, a = bcosC...

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  12. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

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  13. For veca = hat(i) + hat(j), vecb = -hat(i) + 2hat(k), vecc = hat(j) + ...

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  14. Prove the following by vector method. The diagonals of a rhombus are a...

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  15. Determine the sine of the angle between the vectors hat-3hatj+hatk, ha...

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  16. Find the volume of the parallelopiped whose sides are given by the vec...

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  17. Find the value of lambda for which the three points with position vect...

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  18. Find a unit vector perpendicular to the following two vectors veca =2...

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  19. Find the value of lambda so that three vectors veca=2hati-hatj+hatk, ...

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

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