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i) bar(a), bar(b), bar(c) are pairwise n...

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)`.

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The correct Answer is:
`alpha = - 1 and beta = - 1 `
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bar(a), bar(b) , bar(c ) are pair wise 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 vector bar(a) + bar(b) + bar(c ) .

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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.

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.

Show that the following vectors are linearly dependent bar(a)-2bar(b)+bar(c), 2bar(a)+bar(b)-bar(c), 7bar(a)-4bar(b)+bar(c) where bar(a), bar(b), bar(c) are non-coplanar vectors

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VIKRAM PUBLICATION ( ANDHRA PUBLICATION)-ADDITION OF VECTORS -Exercise - 4 (a)
  1. If the vectors - 3 bar(i) + 4 bar(j) + lambda bar(k) and mu bar(i)+ 8...

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  2. ABCDE is a pentagon. If the sum of the vectors bar(AB),bar(AE), bar(...

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  3. If the position vectors of the points A,B,C are -2bar(i)+bar(j)-bar(...

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  4. If bar(OA) = bar(i) + bar(j)+ bar(k), bar(AB) = 3bar(i)-2bar(j)+bar(k)...

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  5. If bar(a) = 2bar(i)+5bar(j)+bar(k) and bar(b) = 4bar(i)+mbar(j)+nbar(k...

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  6. Let bar(a) = 2bar(i) +4bar(j)-5bar(k), bar(b) = bar(i)+bar(j)+bar(k), ...

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  7. If the triangle formed by the vectors 3 bar(i) + 5 bar(j) + 2 bar(k) ,...

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  8. If alpha, beta and gamma be the angle made by the vector 3bar(i)-6bar(...

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  9. Find the angles made by the straight line passing through the points (...

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  10. i) bar(a), bar(b), bar(c) are pairwise non zero and non collinear vect...

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  11. bar(a), bar(b), bar(c) are non-coplanar vectors. Prove thate the follo...

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  12. bar(a) , bar(b), bar (c ), are non-coplanar vectors, Prove that the fo...

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  13. If bar(i), bar(j), bar(k) are unit vectors along the positive directio...

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  14. If bar(a), bar(b), bar(c) are non coplanar vectors, then test for the ...

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  15. If bar(a), bar(b), bar(c) are non coplanar vectors, then test for the ...

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  16. If bar(a), bar(b), bar(c) are non coplanar vectors, then test for the ...

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  17. In the cartesian plane, O is the origin of the coordinate axes. A pers...

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  18. The points O, A, B, X and Y are such that bar(OA)=bar(a), bar(OB)=bar(...

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  19. In DeltaOAB, E is the midpoint of AB and F is a point on OA such that ...

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  20. The point 'E' divides the segment PQ internally in the ratio 1 : 2 and...

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