JEE Main 23 Jan 2025 Shift 1 Paper

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

^

i

+2

^

j

+

^

k

,‌‌

^

i

+3

^

j

−2

^

k

and 2

^

i

+

^

j

−

^

k

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 ‌

√110

3

and the volume of the tetrahedron is ‌

√805

6√2

, then the position vector of E is