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Find the position vector of the point which divides the line joining the points `3bar(a)-4bar(b) and 4bar(a)-3bar(b)` in the ratio 2 : 3 (i) internally and (ii) externally.

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The correct Answer is:
(i) `(17bar(a)-18bar(b))/5`
(ii) `bar(a)-6bar(b)`
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Consider two points P and Q with position vectors bar(OP) = 3bar(a) - 2bar(b) and bar(OQ) = bar(a)+bar(b) . Find the position vector of a point R which divides the line joining P and Q in the ratio 2:1 (i) internally.

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AAKASH SERIES-PROPERTIES OF VECTORS-PRACTICE EXERCISES
  1. Find the position vector of the point which divides the line joining t...

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  2. If bar(OA)=bar(i)+2bar(j)-3bar(k), bar(OB)=3bar(i)-2bar(j)+5bar(k) and...

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  3. If the position vectors of A, B are 2bar(i)-9bar(j)-4bar(k), 6bar(i)-3...

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  4. If (bar(a), bar(i))=(bar(a), bar(j))=pi/4" then "(bar(a), bar(k))=

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  5. Unit vector making angles pi/3, pi/3, (3pi)/4 with bar(i), bar(j), bar...

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  6. If bar(a)=bar(i)+bar(j)+bar(k), bar(b)=2bar(i)+3bar(j), bar(c)=3bar(i)...

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  7. If bar(alpha)=2bar(i)+3bar(j), bar(beta)=4bar(i)+bar(j), bar(gamma)=5b...

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  8. bar(a), bar(b), bar(c) are three vectors of which every pair is non-co...

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  9. Let a, b, g be the distinct real numbers. The points with position vec...

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  10. If the position vectors of the four points A, B, C, D are 2bar(a), bar...

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  11. If the position vectors of three consecutive vertices of a parallelogr...

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  12. A set of vectors bar(a)(1), bar(a)(2), ………, bar(a)(n) is said to linea...

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  13. If 4bar(i)+7bar(j)+8bar(k), 2bar(i)+3bar(j)+4bar(k), 2bar(i)+5bar(j)+7...

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  14. If A=(1, 1, 1), B=(1, 2, 3), C=(2, -1, 1) be the vertices of a DeltaAB...

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  15. If A is the point bar(a)+2bar(b), P is the point bar(a) and P devides ...

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  16. The ratio in which 3bar(i)+4bar(j)+7bar(k) divides the join of bar(i)+...

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  17. In a DeltaOAB, E is the mid point of OB and D is a point in AB such th...

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  18. If 2bar(i)+3bar(j)+5bar(k), 2bar(i)+4bar(j)+5bar(k) and 2bar(i)+4bar(j...

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  19. 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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  20. In a DeltaABC, P.V.'s of A, mid-point of BC are bar(i)+2bar(j)+3bar(k)...

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  21. If G is the centroid of DeltaABC then bar(GA)+bar(GB)+bar(GC)=

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