The position vectors of the vertices, A, B and C of a tetrahedron are `hati + hatj + hatk , hati and 3 hati` respectively. The altitude from vertex D to the opposite face ABC meets the median line through A of triangle ABC at a point E. if the length of the side AD is 4 and the volume of the tetrahedron is `2sqrt2 // 3` find teh position vectors of the point E for all its possible positions .

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

The position vectors of the vertices A, B and C of triangle are hati+hatj, hatj+hatk and hati+hatk , respectively. Find the unit vectors hatr lying in the plane of ABC and perpendicular to IA , where I is the incentre of the triangle.

The position vectors of the points A,B, and C are hati+2hatj-hatk, hati+hatj+hatk , and 2hati+3hatj+2hatk respectively. If A is chosen as the origin, then the position vectors B and C are

The position vectors of the vertices of a triangle are hati+2hatj+3hatk,3hati-4hatj+5hatk" ""and" -2hati+3hatj-7hatk. Find the perimeter of the triangle

The positiion vectors of two point masses 10 kg and 5 kg are (3hati+2hatj+4hatk)m and (3hati+6hatj+5hatk)m respectively. Locate the position of center of mass.

The postion vectors of the four angular points of a tetrahedron are A(hatj+2hatk),B(3hati+hatk),C(4hati+3hatj+6hatk) and D(2hati+3hatj+2hatk) find the volume of the tetrahedron ABCD.

The postion vectors of the four angular points of a tetrahedron are A(hatj+2hatk),B(3hati+hatk),C(4hati+3hatj+6hatk) and D(2hati+3hatj+2hatk) find the volume of the tetrahedron ABCD.