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Show that veca, vecb and vec c are copla...

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

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

If veca , vecb and vecc are non-zero vectors, then vecaxxvecb = vecaxxvecc

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|

If veca.vecb = vecc.veca for all vectors veca , then

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 .

Three vectors veca, vecb and vecc satisfy the condition veca + vecb + vecc = 0 . Find the value of veca.vecb + vecb.vecc + vecc.veca if |veca| = 1, |vecb|= 4, |vecc|= 2 .

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

If veca,vecb and vecc are three vectors such that |veca|=5,|vecb|=12,|vecc|=13 and veca+vecb+vecc=0 then find the value of veca.vecb+vecb.vecc+vecc.veca.

SHARAM PUBLICATION-VECTORS-EXAMPLE
  1. If veca = 3hati+hatj-2hatk, vecb = 2hati-3hatj+4hatk then verify that ...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. If the vertices A,B,C of a triangle ABC are at (1,1,2),(2,2,3),(3,-1,-...

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  19. If vecaxxvecb = vecbxxvecc ne vec0, prove that veca+vecc = mvecb, wher...

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  20. Prove analytically : The perpendicular bisector of the sides of a tria...

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