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Let the position vectors of the vertices A, B and C of a tetrahedron ABCD be k ˆ j ˆ 2 i ˆ + + , k ˆ 2 j ˆ 3 i ˆ − + and k ˆ j ˆ i ˆ 2 − + respectively. The altitude from the vertex D to the opposite face ABC meets the median line segment through A of the triangle ABC at the point E. If the length of AD is 3 110 and the volume of the tetrahedron is 2 6 805 , then the position vector of E is

1. ) k ˆ 7 j ˆ 4 i ˆ ( 2 1 + +
2. ) k ˆ 3 j ˆ 4 i ˆ 7 ( 12 1 + +
3. ) k ˆ j ˆ 12 i ˆ 12 ( 6 1 + +
4. ) k ˆ j ˆ 12 i ˆ 7 ( 6 1 + +

Correct answer: ) k ˆ j ˆ 12 i ˆ 7 ( 6 1 + +

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