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Show that vecaxx(vecb+vecc)+vecbxx(vecc+...

Show that `vecaxx(vecb+vecc)+vecbxx(vecc+veca)+veccxx(veca+vecb)=vec0.`

A

`2|veca||vecb||vecc|`

B

`theta`

C

1

D

`veca+vecb+vecc`

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The correct Answer is:
B
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If veca , vecb and vecc are three vectors such that vecaxx vecb =vecc, vecb xx vecc= veca, vecc xx veca =vecb then prove that |veca|= |vecb|=|vecc|

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If veca, vecb,vecc and vecd are distinct vectors such that veca xx vecc = vecb xx vecd and veca xx vecb = vecc xx vecd . Prove that (veca-vecd).(vecc-vecb)ne 0, i.e., veca.vecb + vecd.vecc nevecd.vecb + veca.vecc.

If veca =2veci+3vecj-veck , vecb =2veci+5veck , vecc =vecj-3veck , verify that vecaxx(vecbxxvecc)=(veca.vecc)vecb-(veca.vecb)vecc .

If veca,vecb, vecc and veca',vecb',vecc' are reciprocal system of vectors, then prove that veca'xxvecb'+vecb'xxvecc'+vecc'xxveca'=(veca+vecb+vecc)/([vecavecbvecc])

If the vectors veca,vecb,vecc form the sides BC,CA and AB respectively of a triangle ABC then (A) veca.(vecbxxvecc)=vec0 (B) vecaxx(vecbxvecc)=vec0 (C) veca.vecb=vecc=vecc=veca.a!=0 (D) vecaxxvecb+vecbxxvecc+veccxxvecavec0

PREMIERS PUBLISHERS-Vector Algebra -I-Choose Correct Option
  1. For any two vectors veca and vecb|veca X vecb|^(2)+|veca.vecb| is:

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  2. If veca,vecb and vecc are three unit vectors satisfying veca-vecb-sqrt...

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  3. Show that vecaxx(vecb+vecc)+vecbxx(vecc+veca)+veccxx(veca+vecb)=vec0.

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  4. Two vertices of a triangle hence position vetors 2veci+4vecj-5veck and...

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  5. If 2veca+6vecb and 3veca+mvecb are parallel then the vector of m is:

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  6. Match the following

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  7. Find the incorrect statement

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  8. Find the incorrect statement

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  9. Find the correct statement

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  10. Find the correct statement: Given vec OA =veca, vecOB=vecb and vecOP =...

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  11. The vectors veca-vecb,vecb-vecc,vecc-veca are

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  12. Find the odd man out.

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  13. Find which in suitable for the blank space given below:|veca.vecb|…….....

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  14. Assertion If D is the midpoint of the side BC of a triangle ABC then v...

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  15. Assertion If G is the centroid of the triangle ABC then vecGA+vecGB+v...

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  16. Find (veci+vecj).{(vecj+veck) X (veck+veci)}:

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  17. If veca +5vecb and 4veca+mvecbare parallel then m is :

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  18. If the projection of veca on vecb and projection of vecb on veca ar...

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  19. If 60^(@), 45^(@), alpha^(@)are the directional angles of a vector vec...

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  20. If aplha, beta, gamma are the directional angles of a vector then sin^...

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