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i) If bar(a), bar(b), bar(c) are non cop...

i) If `bar(a), bar(b), bar(c)` are non coplanar vectors, then prove that the vectors `5bar(a)-6bar(b)+7bar(c), 7bar(a)-8bar(b)+9bar(c) and bar(a)-3bar(b)+5bar(c)` are coplanar.

A

Collinear

B

Coplanar but non collinear

C

non coplanar

D

cannot be determined

Text Solution

Verified by Experts

The correct Answer is:
B
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AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - II
  1. The points with P.V's bar(i)+2bar(j)+bar(k), 2bar(i)+3bar(j)+4bar(k) a...

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  2. The points 2bar(a)+3bar(b)+bar(c), bar(a)+bar(b), 6bar(a)+11bar(b)+5ba...

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  3. i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that...

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  4. If bar(a), bar(b), bar(c) are non coplanar then the vectors bar(a)-2ba...

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  5. The vectors 2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+ba...

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  6. Let bar(a)=bar(i)+bar(j), bar(b)=bar(j)+bar(k) and bar(c)=alphabar(a)+...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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