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

If `xbar(a)+ybar(b)+zbar(c),xbar(b)+ybar(c)+zbar(a),xbar(c)+ybar(a)+zbar(b)=bar(0)" where "bar(a), bar(b), bar(c)` are non-coplanar, then (x, y, z) =

A

(0, 0, 0)

B

(1, 3, 5)

C

(1, -3, 2)

D

(3, 1, 1)

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The correct Answer is:
A
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Find a linear relation between the vectors bar(a)+3bar(b)+4bar(c), bar(a)-2bar(b)+3bar(c), bar(a)+5bar(b)-2bar(c) and 6bar(a)+14bar(b)+4bar(c)" where "bar(a), bar(b), bar(c) are non coplanar vectors.

Find the point of intersection of the line bar(r)=2bar(a)+bar(b)+t(bar(b)-bar(c)) and the plane bar(r)=bar(a)+x(bar(b)+bar(c))+y(bar(a)+2bar(b)-bar(c)) where bar(a), bar(b), bar(c) are non coplanar vectors.

i) bar(a), bar(b), bar(c) are pairwise non zero and non collinear vectors. If bar(a)+bar(b) is collinear with bar(c) and bar(b)+bar(c) is collinear with bar(a) then find the vector bar(a)+bar(b)+bar(c) . ii) If bar(a)+bar(b)+bar(c)=alphabar(d), bar(b)+bar(c)+bar(d)=betabar(a) and bar(a), bar(b), bar(c) are non coplanar vectors, then show that bar(a)+bar(b)+bar(c)+bar(d)=bar(0) .

Show that the points whose P,V are -2bar(a)+3bar(b)+5bar(c ), bar(a)+2bar(b)+3bar(c ) , 7bar(a)-bar(c ) are collinear, where bar(a),bar(b), bar(c ) are non-coplanar vectors.

AAKASH SERIES-PROPERTIES OF VECTORS-EXERCISE - II
  1. If bar(a)=2bar(i)-bar(j)+3bar(k), bar(b)=-bar(i)+4bar(j)-2bar(k), bar(...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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  18. If D, E, F are the midpoints of BC, CA, AB of Delta ABC, then vec(A)D ...

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  19. If D, E and F are respectively the mid-points of AB, AC and BC in Delt...

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  20. If ABCD is a parallelogram then bar(AC)+bar(BD)=

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