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

The vectors `2bar(i)-3bar(j)+bar(k), bar(i)-2bar(j)+3bar(k), 3bar(i)+bar(j)-2bar(k)`

A

Collinear

B

Coplanar but non collinear

C

non coplanar

D

cannot be determined

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Verified by Experts

The correct Answer is:
B
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Find the volume of the parallelopiped having co-tenninus edges are represented by the vectors 2 bar(i) - 3bar(j) + bar(k), bar(i) -bar(j) +2bar(k), 2bar(i) + bar(j) -bar(k) .

Show that the points -2bar(i)+3bar(j)+6bar(k), 6bar(i)-2bar(j)+3bar(k), 3bar(i)+6bar(j)-2bar(k) form an equilateral triangle.

Find t, for which the vectors 2bar(i) - 3bar(j) + bar(k), bar(i) + 2bar(j) -3bar(k) , bar(j) - tbar(k) are coplanar.

Write the position vector of the centroid of the triangle formed by the points whose position vectors are 3bar(i)+2bar(j)-bar(k), 2bar(i)-2bar(j)+5bar(k), bar(i)+3bar(j)-bar(k) .

Find the position vector of the centroid of the tetrahedron formed by the points 2bar(i)-bar(j)-3bar(k), 4bar(i)+bar(j)+3bar(k), 3bar(i)+2bar(j)-bar(k), bar(i)+4bar(j)+2bar(k) .

Show that the triangle formed by the vectors 3bar(i)+5bar(j)+2bar(k), 2bar(i)-3bar(j)-5bar(k), -5bar(i)-2bar(j)+3bar(k) is equilateral.

Find the vector area and area of the triangle with vertices bar(i) + bar(j)-bar(k), 2bar(i)- 3bar(j) + bar(k), 3 bar(i) + bar(j)- 2bar(k) .

The P.V.'s of the vertices of a triangle are 2bar(i)+3bar(j)+4bar(k), 4bar(i)+6bar(j)+3bar(k), 3bar(i)+2bar(j)+3bar(k) P.V. of its orthocentre is

Show that the points A(2bar(i)-bar(j)+bar(k)), B(bar(i)-3bar(j)-5bar(k)), C(3bar(i)-4bar(j)-4bar(k)) are the vertices of a right angled triangle.

If the position vectors of the points A,B,C are -2bar(i)+bar(j)-bar(k), -4bar(i)+2bar(j)+2bar(k), 6bar(i)-3bar(j)-13bar(k) respectively and bar(AB) = lambda bar(AC) then find the value of lambda .

AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - II
  1. i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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