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If bar(a)=bar(i)+bar(j)+bar(k), bar(b)=4...

If `bar(a)=bar(i)+bar(j)+bar(k), bar(b)=4bar(i)+3bar(j)+4bar(k), bar(c)=bar(i)+alphabar(j)+betabar(k)` are linearly dependent vectors and `abs(bar(c))=sqrt(3)` then

A

`alpha=1, beta=-1`

B

`alpha=1, beta=pm1`

C

`alpha=-1, beta=pm1`

D

`alpha=pm1, beta=1`

Text Solution

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The correct Answer is:
D
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AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - II
  1. Let bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k) and bar(c)=alphabar(a)+...

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  2. The number of distinct real values of lambda for which the vectors -la...

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  3. If bar(a)=bar(i)+bar(j)+bar(k), bar(b)=4bar(i)+3bar(j)+4bar(k), bar(c)...

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  4. If bar(a)=2bar(i)-bar(j)+3bar(k), bar(b)=-bar(i)+4bar(j)-2bar(k), bar(...

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  5. If the points A(bar(a)), B(bar(b)), C(bar(c)) satisfy the relation 3ba...

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  6. If xbar(a)+ybar(b)+zbar(c),xbar(b)+ybar(c)+zbar(a),xbar(c)+ybar(a)+zba...

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  7. If bar(r)=3bar(i)+2bar(j)-5bar(k), bar(a)=2bar(i)-bar(j)+bar(k), bar(b...

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  8. The vector of magnitude 3sqrt(6) along the bisector of the angle betwe...

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  9. The vector abar(i)+b""bar(j)+cbar(k) is a bisector of the angle betwee...

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  10. If the vector -bar(i)+bar(j)-bar(k) bisects the angles between the vec...

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  11. If A(1, -1, -3), B(2, 1, -2), C(-5, 2, -6) are the vertices of a Delta...

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  12. The median AD of the triangle ABC is bisected at E. BE meets AC in F t...

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  13. If S is the circumcentre, G the centroid, O the orthocentre of Delta A...

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  14. If S is the circumcentre, O is the orthocentre of Delta ABC then vec(O...

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  15. The P.V.'s of the vertices of a DeltaABC are bar(i)+bar(j)+bar(k), 4ba...

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  16. The P.V.'s of the vertices of a triangle are 2bar(i)+3bar(j)+4bar(k), ...

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  17. DeltaABC be an equilateral triangle whose orthocentre is the origin 'O...

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  18. The P.V.'s of A, B, C are bar(i)+bar(j)+bar(k), 4bar(i)+bar(j)+bar(k),...

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  19. In a DeltaABC, P.V.'s of midpoints of AB, AC are bar(i)-bar(j)+bar(k),...

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  20. The vectors of bar(AB)=3bar(i)+4bar(k) and bar(AC)=5bar(i)-2bar(j)+4ba...

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