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If vecaxxvecb=vecc and vecbxxvecc=veca, ...

If `vecaxxvecb=vecc and vecbxxvecc=veca, show that veca,vecb,vecc` are orthogonal in pairs. Also show that |vecc|=|veca| and |vecb|=1`

A

`|veca|=1,vecb=vecc`

B

`|vecc|=1,|veca|=1`

C

`|vecb|=2,vecc=2veca`

D

`|vecb|=1,|vecc|=|veca|`

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OBJECTIVE RD SHARMA ENGLISH-SCALAR AND VECTOR PRODUCTS OF THREE VECTORS -Exercise
  1. If veca,vecb and vecc are non coplanar and unit vectors such that veca...

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

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  3. If vecaxxvecb=vecc and vecbxxvecc=veca, show that veca,vecb,vecc are o...

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  4. Let veca , vecb and vecc be vectors forming right- hand triad . Let ve...

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  5. vecrxxveca=vecbxxveca,vecrxxvecb=vecaxxvecb,vecanevec0,vecbnevec0,veca...

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  6. The vector veca coplanar with the vectors hati and hatj perendicular t...

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  7. If the vectors veca and vecb are mutually perpendicular, then veca xx ...

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  8. If veca, vecb, vecc are non-coplanar non-zero vectors, then (vecaxxv...

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  9. Let veca=hati-hatj, vecb=hatj-hatk, vecc=hatk-hati. If hatd is a unit ...

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  10. If the vectors (sec^(2)A)hati+hatj+hatk, hati+(sec^(2)B)hatj+hatk,hati...

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  11. x and y are two mutually perpendicular unit vector, if the vectors aha...

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  12. The three concurrent edges of a parallelopiped represent the vectors ...

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  13. If a=hati+hatj+hatk,b=hati+hatj,c=hati and (axxb)xxc=lamda a+mub, then...

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  14. If veca=2hati-3hatj+5hatk , vecb=3hati-4hatj+5hatk and vecc=5hati-3hat...

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  15. If veca,vecb,vecc are linearly independent vectors, then ((veca+2vecb)...

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  16. If veca,vecb are non-collinear vectors, then [(veca,vecb,hati)]hati+[...

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  17. If [(2veca+4vecb,vecc,vecd)]=lamda[(veca,vecc,vecd)]+mu[(vecb,vecc,vec...

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  18. If the volume of the tetrahedron whose vertices are (1,-6,10),(-1,-3,7...

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  19. (vecbxxvecc)xx(veccxxveca)=

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  20. When a right handed rectangular Cartesian system OXYZ is rotated about...

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