\[\boxed{\mathbf{668.}ОК\ ГДЗ\ –\ домашка\ на\ 5}\]
\[Найдем\ длины\ сторон\ каждого\ \]
\[треугольника\ по\ формуле:\]
\[\textbf{а)}\ A(9;3; - 5);\ \ B(2;10; - 5);\ \ \]
\[C(2;3;2).\]
\[\left| \text{AB} \right| = \left| \text{BC} \right| = \left| \text{AC} \right| -\]
\[равносторонний\ треугольник.\]
\[\textbf{б)}\ A(3;7; - 4);\ \ B(5; - 3;2);\ \ \]
\[C(1;3; - 10).\]
\[\left| \text{AB} \right| = \left| \overrightarrow{\text{AB}} \right| =\]
\[= \sqrt{(5 - 3)^{2} + ( - 3 - 7)^{2} + (2 + 4)^{2}} =\]
\[= \sqrt{140};\]
\[\left| \text{AB} \right|^{2} + \left| \text{AC} \right|^{2} = 140 + 56 =\]
\[= 196 = \left| \text{AC} \right|^{2}.\]
\[\mathrm{\Delta}ABC - прямоугольный;\ \]
\[\angle A = 90{^\circ}.\]
\[\textbf{в)}\ A(5; - 5; - 1);\ \ B(5; - 3; - 1);\ \ \]
\[C(4; - 3;0).\]
\[\left| \text{AB} \right|^{2} + \left| \text{BC} \right|^{2} = 4 + 2 = 6 =\]
\[= \left| \text{AC} \right|^{2}.\]
\[⊿ABC - прямоугольный;\ \ \]
\[\angle B = 90{^\circ}.\]
\[\textbf{г)}\ A( - 5;2;0);\ \ B( - 4;3;0);\ \ \]
\[C( - 5;2; - 2).\]
\[\left| \text{AB} \right|^{2} + \left| \text{AC} \right|^{2} = 2 + 4 = 6 =\]
\[= \left| \text{BC} \right|^{2}.\]
\[⊿ABC - прямоугольный;\ \]
\[\angle A = 90{^\circ}.\]