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The position vectors of the vertices A, ...

The position vectors of the vertices A, B and C of a tetrahedron ABCD are `hat i + hat j + hat k`, `hat k `, `hat i` and `hat 3i`,respectively. The altitude from vertex D to the opposite face ABC meets the median line through Aof triangle ABC at a point E. If the length of the side AD is 4 and the volume of the tetrahedron is2/2/3, find the position vectors of the point E for all its possible positfons

A

`3hati-hatj-hatk`

B

`-hati+3hatj+3hatk`

C

`3hati-3hatj-hatk`

D

`-hati+3hatj+hatk`

Text Solution

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The correct Answer is:
A, B
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FIITJEE-VECTOR-ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-II
  1. ABCD is a rhombus IF M,N,P are points taken on sides AB,BC,CD respecti...

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  2. Three points having position vectors bara,barb and barc will be collin...

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  3. IF bara,barb,barc and bard are any four vectors then (bara times barb)...

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  4. A line passes through the points whose position vectors are hati+hatj-...

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  5. IF barx times barb=barc times barb and barx . bara =0 then barx=

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  6. IF |bara|=4,|barb|=2 and the angle between bara and barb is pi/6 then ...

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  7. The position vectors of the vertices A, B and C of a tetrahedron ABCD ...

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  8. If vec(DA)=veca,vec(AB)=vecb and vec(CB)=kveca where kgt0 and X,Y are ...

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  9. If barc=bara times barb and barb=barc times bara then

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  10. If bara,barb and barc are non coplanar vectors such that barb times ba...

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  11. The position vectors of the vertices, A,B,C of a tetrahedron ABCD are ...

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  12. Let bara,barb and barc are three mutually perpendicular unit vectors a...

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  13. Let veca = hati + hatj + hatk and let vecr be a variable vector such t...

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  14. Let barlamda=bara times (barb +barc), barmu=barb times (barc+bara) and...

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  15. Let bara,barb,barc be three coplanar unit vectors such that bara+barb+...

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  16. For three non-coplanar vectors bara,barb,barc the relation |(bara time...

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  17. If bara=hati+hatj+hatk , bara.barb=2 and bara times barb=2hati+hatj-3h...

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  18. Let bara.barb and barc are three unit vectors such that |bara+barb+bar...

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