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If 'O' is circumcente and 'H' is orthoce...

If 'O' is circumcente and 'H' is orthocentre of `DeltaABC`, then
`{:("List-I", "List-II"), ("A) "bar(OA)+bar(OB)+bar(OC), "1) "1/2bar(HO)), ("B) "bar(HA)+bar(HB)+bar(HC), "2) "2bar(HO)), ("C) "bar(AH)+bar(HB)+bar(HC), "3) "2bar(AO)), ("D) "bar(OG), "4) "1/3bar(OH)), ("", "5) "bar(OH)):}`
The correct matching is

A

`{:(A, B, C, D), (1, 5, 3, 2):}`

B

`{:(A, B, C, D), (5, 2, 4, 3):}`

C

`{:(A, B, C, D), (5, 2, 3, 4):}`

D

`{:(A, B, C, D), (2, 4, 3, 5):}`

Text Solution

Verified by Experts

The correct Answer is:
C
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AAKASH SERIES-PROPERTIES OF VECTORS-PRACTICE EXERCISES
  1. The vector equation of the plane passing through the point 2bar(i)+2ba...

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  2. The vector equation of the plane passing through the origin and the po...

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

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  4. The vector equation of the line passing through the point 2bar(i)+bar(...

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  5. If A(bar(i)+2bar(j)+3bar(k)), B(-bar(i)-bar(j)+8bar(k)), C(-4bar(i)+4b...

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  6. A point on the line bar(r)=(1-t)(2bar(i)+3bar(j)+4bar(k))+t(3bar(i)-...

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  7. The point of intersection of the lines bar(r)=bar(a)+t(bar(b)+bar(c)),...

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  8. The point P on the line passing through A(3bar(i)+2bar(j)-3bar(k)) and...

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  9. The point of intersection of the plane bar(r)=(bar(a)-bar(b))+s(bar(a)...

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  10. If 'O' is circumcente and 'H' is orthocentre of DeltaABC, then {:("L...

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  11. The vector bar(i)+xbar(j)+3bar(k) is rotated through angle theta and d...

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

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  13. Consider the points A, B, C and D with P.V.'s 7bar(i)-4bar(j)+7bar(k),...

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  14. i) If bar(a), bar(b), bar(c) are non coplanar vectors, then prove that...

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  15. If bar(a)=i+j+k, bar(b)=i-j+2k and bar(c)=x""i+(x-2)j-k. If the vector...

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

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  17. If C is the mid point of AB and P is any point outside AB, then

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  18. If bar(i)+2bar(j)+3bar(k), 3bar(i)+2bar(j)+bar(k) are sides of a paral...

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  19. Let ABC be a triangle whose circumcentre is at P. If the position vect...

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  20. Let a, b and c be distinct non-negative numbers. If the vectors abar(i...

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