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If veca=hati+hatj+hatk, hatb4hati+3hatj+...

If `veca=hati+hatj+hatk, hatb4hati+3hatj+4hatk and vecc=hati+alphahatj+beta hatk` are linearly dependent vectors and `|vecc|=sqrt(3)` then (A) `alpha=1, beta=-1` (B) `alpha=1,beta=+-1` (C) `alpha-1,beta=+-1` (D) `alpha=+-1,beta=1`

A

`alpha = 1 , beta = -1`

B

`alpha = 1, beta = pm 1`

C

`alpha = -1 , beta = pm 1`

D

`alpha = pm1 , beta = 1`

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The correct Answer is:
D
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DISHA PUBLICATION-VECTOR ALGEBRA-EXERCISE -1 : CONCEPT BUILDER
  1. If veca=hati+hatj+hatk, hatb4hati+3hatj+4hatk and vecc=hati+alphahatj+...

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  2. In a triangle ABC three forces of magnitudes 3vec(AB), 2vec(AC) and 6v...

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  3. If |veca + vecb| = |veca - vecb| then the vectors veca and vecb are ad...

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  4. If the position vectors of the vertices A,B and C of a DeltaABC are 7h...

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

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  6. The vectors vec(AB)=3hati+4hatk and vec(AC)=5hati-2hatj+4hatk are the ...

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  7. If two vertices of a triangle are i-j and j+k , then the third vertex ...

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  8. The figure formed by the four points hati + hatj -hatk, 2hati + 3hatj,...

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  9. If the vector 8hati+ahatj of magnitude 10 is the directionn of the vec...

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  10. If A, B, C are vertices of a triangle whose position vectors are vec ...

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  11. Which of the following is an example of two different vectors with sam...

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  12. veca=3hati-5hatj and vecb=6hati+3hatj are two vectors and vec c is a v...

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  13. If vecp,vecq and vecr are perpendicular to vecq + vecr , vec r + vecp...

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  14. If veca =hati + hatj - hatk, vecb = 2hati + 3hatj + hatk and vec c = h...

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  15. If hat(i)+hat(j), hat(j)+hat(k), hat(i)+hat(k) are the position vector...

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  16. If veca and vecb are non colinear vectors, then the value of alpha for...

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  17. If angle between veca = hati - 2hatj + 3hatk and vecb = 2hati + hatj ...

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  18. If veca, vecb,vecc are non-coplanar vectors and lambda is a real numbe...

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  19. Find the unit vector parallel to the resultant vector of 2hati+4hatj-5...

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  20. If the middle points of sides BC, CA and AB of triangle ABC are respec...

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