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If A(bar(i)+2bar(j)+3bar(k)), B(-bar(i)-...

If `A(bar(i)+2bar(j)+3bar(k)), B(-bar(i)-bar(j)+8bar(k)), C(-4bar(i)+4bar(j)+6bar(k))` are the vertices of a triangle then the equation of the line passing through the circumcentre and parallel to `bar(AB)` is

A

`bar(r)=(-4/3bar(i)+5/3bar(j)+17/3bar(k))+t(2bar(i)+3bar(j)-5bar(k))`

B

`bar(r)=(2bar(i)+3bar(j)+5bar(k))+t(2bar(i)-3bar(j)-5bar(k))`

C

`bar(r)=(4/3bar(i)-5/3bar(j)-17/3bar(k))+t(2bar(i)-3bar(j)+5bar(k))`

D

`bar(r)=(-4/3bar(i)-5/3bar(j)-17/3bar(k))+t(2bar(i)+3bar(j)+5bar(k))`

Text Solution

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The correct Answer is:
A
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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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