In space, points \(A(-1;4;0)\), \(B(-3;-4;4)\), \(C(11;0;-6)\) are given. Point \(M\) is the midpoint of segment \(BC\). Find the coordinates of vector \(\vec{AM}\). Write the sum of the vector coordinates in the answer.
Three vertices of parallelogram \(ABCD\) are given: \(A(1;-3;2)\), \(B(-5;1;0)\), \(C(5;7;-6)\). Point \(O\) is the center of the parallelogram. Find the coordinates of vector \(\vec{OB}\). Write the sum of the vector coordinates in the answer.
Three vertices of parallelogram \(ABCD\) are given: \(A(5;-1;0)\), \(B(-5;3;2)\), \(C(2;2;-2)\). Find the coordinates of vertex \(D\). Write the sum of its coordinates in the answer.
A sphere is given by the equation \((x-3)^2+(y+2)^2+(z-6)^2=16\). Find the distance from the origin to the closest point of the sphere.
The vertices of triangle \(DEF\) are \(D(1;3;5)\), \(E(3;1;-1)\), \(F(2;-1;-2)\). Find the length of the median \(FM\).