The midpoint of segment \(BC\) is \(M\left(\dfrac{-3+11}{2};\dfrac{-4+0}{2};\dfrac{4+(-6)}{2}\right)=(4;-2;-1)\).

Then \(\vec{AM}=(4-(-1);-2-4;-1-0)=(5;-6;-1)\).

The sum of the coordinates is \(5-6-1=-2\).

Answer: \(-2\).

The center of the parallelogram is the midpoint of diagonal \(AC\): \(O\left(\dfrac{1+5}{2};\dfrac{-3+7}{2};\dfrac{2+(-6)}{2}\right)=(3;2;-2)\).

Then \(\vec{OB}=(-5-3;1-2;0-(-2))=(-8;-1;2)\).

The sum of the coordinates is \(-8-1+2=-7\).

Answer: \(-7\).

For a parallelogram with consecutive vertices, \(D=A+C-B\).

So \(D(5+2-(-5);-1+2-3;0+(-2)-2)=(12;-2;-4)\).

The sum of the coordinates is \(12-2-4=6\).

Answer: \(6\).

The center of the sphere is \((3;-2;6)\), and the radius is \(4\).

The distance from the origin to the center is \(\sqrt{3^2+(-2)^2+6^2}=\sqrt{49}=7\).

The closest point of the sphere is at distance \(7-4=3\) from the origin.

Answer: \(3\).

The midpoint of side \(DE\) is \(M\left(\dfrac{1+3}{2};\dfrac{3+1}{2};\dfrac{5+(-1)}{2}\right)=(2;2;2)\).

The vector \(\vec{FM}=(0;3;4)\), so the length of the median is \(\sqrt{0^2+3^2+4^2}=5\).

Answer: \(5\).

For a parallelogram, \(D=A+C-B\).

We get \(D(-2+7-1;5+(-15)-(-3);-1+27-7)=(4;-7;19)\).

Then \(\vec{BD}=(4-1;-7-(-3);19-7)=(3;-4;12)\).

The diagonal length is \(\sqrt{3^2+(-4)^2+12^2}=\sqrt{169}=13\).

Answer: \(13\).

The center of the sphere is \((2;-4;4)\), and the radius is \(3\).

The distance from the origin to the center is \(\sqrt{2^2+(-4)^2+4^2}=\sqrt{36}=6\).

The farthest point of the sphere is at distance \(6+3=9\) from the origin.

Answer: \(9\).

The center of the sphere is the midpoint of the diameter: \(\left(\dfrac{3+1}{2};\dfrac{5+1}{2};\dfrac{9+3}{2}\right)=(2;3;6)\).

The distance to the origin is \(\sqrt{2^2+3^2+6^2}=\sqrt{49}=7\).

Answer: \(7\).

The midpoint of the segment is \(M\left(\dfrac{2+4}{2};\dfrac{-3+(-5)}{2};\dfrac{2+(-2)}{2}\right)=(3;-4;0)\).

Then \(OM=\sqrt{3^2+(-4)^2+0^2}=5\).

Answer: \(5\).

The center of the sphere is the midpoint of the diameter: \(\left(\dfrac{-2+(-6)}{2};\dfrac{5+11}{2};\dfrac{5+(-3)}{2}\right)=(-4;8;1)\).

The distance to the origin is \(\sqrt{(-4)^2+8^2+1^2}=\sqrt{81}=9\).

Answer: \(9\).

The midpoint of segment \(AB\) is \(K\left(\dfrac{5+(-1)}{2};\dfrac{6+(-2)}{2};\dfrac{2+0}{2}\right)=(2;2;1)\).

Then \(\vec{CK}=(2-5;2-0;1-(-4))=(-3;2;5)\).

The sum of the coordinates is \(-3+2+5=4\).

Answer: \(4\).

Find the fourth vertex: \(D=A+C-B=(1+1-(-3);-4+17-2;2+0-(-5))=(5;11;7)\).

Then \(\vec{BD}=(5-(-3);11-2;7-(-5))=(8;9;12)\).

The diagonal length is \(\sqrt{8^2+9^2+12^2}=\sqrt{289}=17\).

Answer: \(17\).

For a parallelogram, \(C=B+D-A\).

Hence \(C(-2+(-3)-0;3+5-5;2+0-2)=(-5;3;0)\).

The sum of the coordinates is \(-5+3+0=-2\).

Answer: \(-2\).

The midpoint of side \(AB\) is \(M\left(\dfrac{1+(-3)}{2};\dfrac{-3+(-1)}{2};\dfrac{6+0}{2}\right)=(-1;-2;3)\).

Then \(\vec{CM}=(-1-5;-2-6;3-3)=(-6;-8;0)\).

The median length is \(\sqrt{(-6)^2+(-8)^2}=10\).

Answer: \(10\).

The center of the sphere is \((1;4;-8)\), and the radius is \(5\).

The distance to the center is \(\sqrt{1^2+4^2+(-8)^2}=\sqrt{81}=9\).

The closest point of the sphere is at distance \(9-5=4\) from the origin.

Answer: \(4\).

The midpoint of segment \(AB\) is \(M\left(\dfrac{-2+0}{2};\dfrac{3+5}{2};\dfrac{6+10}{2}\right)=(-1;4;8)\).

The distance to the origin is \(\sqrt{(-1)^2+4^2+8^2}=\sqrt{81}=9\).

Answer: \(9\).