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

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

A

` vecx=vec0 `

B

` vecy=vec0 `

C

` vecx ` and ` vecy ` are parallel

D

` vecx=vecx ` or ` vecy=vec0 ` or ` vecx ` and ` vecy ` are parallel

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The correct Answer is:
d
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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])

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FULL MARKS-APPLICATIONS OF VECTOR ALGEBRA-Additional Questions Solved
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  3. Find the point of intersection of the line vecr=(vecj-veck)+s(2veci-...

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  4. Find the meeting point of the line vecr=(2veci+vecj-3veck)+t(2veci-v...

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  6. The planes vecr.(2vec+lambdavecj-3veck)=10 and vecr.(lambdavec+3ve...

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  7. Find the angle between the line (x-2)/(3)=(y-1)/(-1)=(z-3)/(2)" and th...

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  8. Find the angle between the line vecr=veci+vecj+3veck+lambda(2veci+ve...

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  9. If veca=2veci+vecj-veck , vecb=veci+2vecj+veck and vecc=veci-v...

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  10. If veca=hati-hatk,vecb=xhati+hatj+(1-x)hatk,vecc=yhati+xhatj+(1+x-y)h...

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  11. If veca , vecb , vecc are three non-coplanar vector and vecp...

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  12. The value of hati.(hatjxxhatk)+hatj.(hatkxxhati)+hatk.(hatjxxhati) ...

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  13. Let a,b,c be distinct non-negative numbers. If the vectors ahati+ahatj...

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  14. The value of hati.(hatjxxhatk)+(hatixxhatk).hatj …….

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  15. The value of [hati - hatj , hatj - hatk, hatk - hati] is :

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

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  17. The area of the parallelogram having diagonals vec(a)=3hat(i)+hat(j)-2...

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

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  19. If bar(PR)=2hat(i)+hat(j)+hat(k),bar(QS)=hat(i)+3hat(j)+2hat(k), then ...

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  20. if (vecaxxvecb)xxvecc=vecaxx(vecbxxvecc) where veca,vecb,vecc ar...

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