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If [veca xx vecb vecb xx vecc vecc xx v...

If `[veca xx vecb vecb xx vecc vecc xx veca]=lambda[veca vecb vecc]^2`, then `lambda` is equal to

A

0

B

1

C

2

D

3

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The correct Answer is:
B
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If alpha(veca xx vecb)+beta(vecb xx vecc)+lambda(vecc xx veca)=0 , then

If the volume of the parallelepiped formed by the vectors veca xx vecb, vecb xx vecc and vecc xx veca is 36 cubic units, then the volume (in cubic units) of the tetrahedron formed by the vectors veca+vecb, vecb+vecc and vecc + veca is equal to

If veca is parallel to vecb xx vecc, then (veca xx vecb) .(veca xx vecc) is equal to (a) |veca|^(2)(vecb.vecc) (b) |vecb|^(2)(veca .vecc) (c) |vecc|^(2)(veca.vecb) (d) none of these

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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. If [veca xx vecb vecb xx vecc vecc xx veca]=lambda[veca vecb vecc]^2,...

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  2. For non-zero vectors veca, vecb and vecc , |(veca xx vecb) .vecc| = |v...

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  3. Let veca=hati+hatj-hatk, vecb=hati-hatj+hatk and vecc be a unit vector...

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  4. If veca lies in the plane of vectors vecb and vecc, then which of the ...

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  5. The value of [(veca-vecb, vecb-vecc, vecc-veca)], where |veca|=1, |vec...

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  6. If veca , vecb , vecc are three mutually perpendicular unit ve...

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  7. If vecr.veca=vecr.vecb=vecr.vecc=0 for some non-zero vectro vecr, then...

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  8. If the vectors ahati+hatj+hatk, hati+bhatj+hatk, hati+hatj+chatk(a!=1,...

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  9. If hata, hatb, hatc are three units vectors such that hatb and hatc ar...

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  10. For any three vectors veca, vecb, vecc the vector (vecbxxvecc)xxveca e...

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  11. for any three vectors, veca, vecb and vecc , (veca-vecb) . (vecb -vecc...

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  12. For any vectors vecr the value of hatixx(vecrxxhati)+hatjxx(vecrxxha...

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  13. If the vectors veca=hati+ahatj+a^(2)hatk, vecb=hati+bhatj+b^(2)hatk, v...

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  14. Let veca,vecb,vecc be three noncolanar vectors and vecp,vecq,vecr are ...

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  15. If vecA, vecB and vecC are three non - coplanar vectors, then (vecA.ve...

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  16. Let veca=a(1)hati+a(2)hatj+a(3)hatk,vecb=b(1)hati+b(2)hatj+b(3)hatk an...

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  17. If non-zero vectors veca and vecb are perpendicular to each ot...

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  18. show that (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) if and only if veca a...

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  19. If veca,vecb, vecc and vecp,vecq,vecr are reciprocal system of vectors...

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  20. vecaxx(vecaxx(vecaxxvecb)) equals

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  21. If veca =hati + hatj, vecb = hati - hatj + hatk and vecc is a unit vec...

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