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If veca,vecb,vecc are linearly independe...

If `veca,vecb,vecc` are linearly independent vectors, then which one of the following set of vectors is linearly dependent?

A

`vec(a) + vec(b) ,vec(b) + vec(c) , vec(c) + vec(a)`

B

`vec(a) - vec(b) , vec(b) - vec(c) , vec(c) - vec(a)`

C

`vec(a) xx vec(b) , vec(b) xx vec(c) , vec(c) xx vec(a)`

D

none of these

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The correct Answer is:
B
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MOTION-VECTOR -EXERCISE - 1
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  3. For a non zero vector vec(A) . If the equations vec(A).vec(B) = vec...

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  5. If vecu=veca-vecb,vecv=veca+vecb and |veca|=|vecb|=2, then |vecuxxvecv...

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  6. If A(1,1,1),C(2,-1,2) the vector equation of the line vec(AB) is v...

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  7. The value of [(veca -2vecb-vecc)(veca-vecb)( veca-vecb-vecc)] is equal...

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  8. The volume of the parallelopiped constructed on the diagonals of the f...

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  9. If vec u , vec va n d vec w are three non-cop0lanar vectors, then ...

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  10. Let overset(to)(a) =a(1) hat(i) + a(2) hat(j) + a(3) hat(k) , overse...

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  11. Vector vec x satisfying the relation vec A . vec x = c and vec B xx v...

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  12. If vec a , vec b ,a n d vec c be non-zero vectors such that no tow...

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  13. The pairs vec a,vec b and vec c,vec d each determines plane. Then the ...

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  14. Consider the vectors, vec(a),vec(b),vec(c),vec(d) such that (vec(a)xxv...

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  15. If veca,vecb,vecc are linearly independent vectors, then which one of ...

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  16. A point taken on each median of a triangle divides the median in the r...

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  17. If G is the centroid of triangle A B C ,t h e n vec G A+ vec G B+ vec ...

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  18. The vector bar(AB)=3hati+4hatk and bar(AC)=5hati-2hatj+4hatk are the s...

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  19. If the vectors vec aa n d vec b are linearly idependent satisfying (s...

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  20. If vec a , vec ba n d vec c are three mutually perpendicular vecto...

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