The position vectors of the vertices A,B and C of a tetrahedron ABCD are ˆi+ˆj+ˆk, ˆi and 3^i respectively. The altitude from vertex D to the opposite face ABC meets the median line through A of the triangle ABC at a point E. If the length of the side AD is 4 and the volume of the tetrahedron is 2√23 cubic units, then the position vector(s) of the point E for all its positions is (are)

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

1.	The position vectors of the vertices A,B and C of a tetrahedron ABCD are ˆi+ˆj+ˆk, ˆi and 3^i respectively. The altitude from vertex D to the opposite face ABC meets the median line through A of the triangle ABC at a point E. If the length of the side AD is 4 and the volume of the tetrahedron is 2√23 cubic units, then the position vector(s) of the point E for all its positions is (are)
Answer» The position vectors of the vertices $A, B$ and $C$ of a tetrahedron $A B C D$ are $ˆ i + ˆ j + ˆ k,$ $ˆ i$ and $3^i$ respectively. The altitude from vertex $D$ to the opposite face $A B C$ meets the median line through $A$ of the triangle $A B C$ at a point $E .$ If the length of the side $A D$ is $4$ and the volume of the tetrahedron is $\frac{2 \sqrt{2}}{3}$ cubic units, then the position vector(s) of the point $E$ for all its positions is (are)

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