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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 positions

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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