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The values of k, for which |k" "veca|lt|...

The values of k, for which `|k" "veca|lt|veca| andkveca+(1)/(2)veca` is parallel to `veca` holds true are……..

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We have, `|k" "veca|lt|veca| andkveca+(1)/(2)veca`
`|kveca|lt|veca|implies|k||veca|lt|veca|`
`implies|k|lt1implies-1ltklt1`
Also, since `kveca+(1)/(2)veca` is parallel to `veca`, then we see that at `k=(-1)/(2),kveca+(1)/(2)veca` becomes a null vector and then it will not be parallel to `veca`.
So, `kveca+(1)/(2)veca` is parallel to `veca` holds true when `kin]-1,1[kne(-1)/(2)`,
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NCERT EXEMPLAR ENGLISH-VECTOR ALGEBRA-OBJECTIVE TPYE QUESTIONS
  1. For any vector veca the value of (vecaxxhati)^2+(vecaxxhatj)^2+(vecaxx...

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  2. If |veca|=10,|vecb|=2andveca.vecb=12, then the value of |vecaxxvecb| i...

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  3. The vectors lamdahati+hatj+2hatk,hati+lamdahatj-hatkand2hati-hatj+lamd...

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  4. If veca,vecbandvecc are unit vectors such that veca+vecb+vecc=0, then ...

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  5. The projection vector of veca" on "vecb is

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  6. If veca,vecbandvecc are three vectors such that veca+vecb+vecc=0and|ve...

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  7. If |veca|=4and-3lelamdale2, then the range of |lamdaveca| is

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  8. The number of vectors of unit length perpendicular to the vectors veca...

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  9. The vector veca+vecb bisects the angle between the non-collinear vecto...

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  10. If vecr.veca=0,vecr.vecb=0andvecr.vecc=0 for some non-zero vector vecr...

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  11. The vectors veca=3hati-2hatj+2hatkandvecb=-hati-2hatk are the adjacent...

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  12. The values of k, for which |k" "veca|lt|veca| andkveca+(1)/(2)veca is ...

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  13. The value of the expression |vecaxxvecb|^(2)+(veca.vecb)^(2) is….. .

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  14. If |vecaxxvecb|^(2)+|veca.vecb|^(2)=144and|veca|=4,"then "|vecb| is eq...

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  15. If veca is any non-zero vector, then (veca.hati)hati+(veca.hatj)hatj+(...

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  16. State true or false: If |veca|=|vecb|, then necessarily it implies vec...

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  17. State true or false: Position vector of a point vecP is a vector whose...

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  18. State true or false: If |veca+vecb|=|veca-vecb|, then the vectors veca...

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  19. The formula (veca+vecb)^(2)=vec(a^(2))+vec(b^(2))+2vecaxxvecb is valid...

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  20. State true or false: If vecaandvecb are adjacent sides of a rhombus, t...

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