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(i) If the position vectors of the poin...

(i) If the position vectors of the points A, B, C be `5hat(i)+3hat(j)+4hat(k), hat(i)+5hat(j)+hat(k) " and " -3hat(i)+7hat(j)-2hat(k)` respectively, then show that the points B bisects the line-segment `bar(AC)`.
(ii) The position vectors of the points P and Q are `5hat(i)-12hat(j)+5hat(k) " and " -4hat(i)+3hat(j)-hat(k)` respectively. Find the position vectors of the trisection points of the line-segment `bar(PQ)`.

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The correct Answer is:
The required position vectors of the trisection points are `2hat(i)-7hat(j)+3hat(k) " and " -hat(i)-2hat(j)-hat(k)`.
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CHHAYA PUBLICATION-VECTOR-ILLUSTRATIVE EXAMPLES
  1. The position vectors of the points A, B, C and D are hat(i)+hat(j)+hat...

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  2. show by vector method that the points (2, -1, 3), (3, -5, 1) and (-1, ...

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  3. Using vector method show that the points (7, 9), (3, -7) and (-3, 3) f...

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  4. The position vectors of the points A,B, and C are 2hat(i)+4hat(j)-hat(...

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  5. Write the direction ratios of the vector 2hat(i)-hat(j)-2hat(k) and he...

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  6. Find a vector of magnitude 14 in the direciton of the vector -3hat(i)+...

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  7. If vec(a) " and "vec(b) are non-collinear vectors and vec(p)=(x+4y)vec...

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  8. Prove that the points with position vectors 60hat(i)+3hat(j), 40hat(i)...

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  9. For the vectors vec(a) " and " vec(b) show that (i) abs(vec(a)+vec(b...

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  10. (i) If the position vectors of the points A, B, C be 5hat(i)+3hat(j)+...

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  11. If the magnitude of difference of two unit vectors in sqrt(3), then sh...

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  12. ABCDEF is a regular hexagon. If vec(AB)=vec(a) " and " vec(BC)=vec(b),...

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  13. Using vector method show that the diagonals of a parallelogram bisect ...

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  14. By vector method prove that the three medians of a triangle are concur...

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  15. Using vector method show that the line joining the middle points of tw...

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  16. If G be the centroid of the triangle ABC, then prove that vec(GA)+vec(...

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  17. ABCD is a quadrilateral and E is the point of intersection of the line...

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  18. By vector method prove that the straight line joining the mid-points o...

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  19. vec(a)=hat(i)+hat(j)+hat(k) " and " vec(b)=2hat(i)+hat(j)+2hat(k) repr...

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  20. Three non-zero vectors vec(a), vec(b), vec(c) are such that no two of ...

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