Категория:Задачник Кузнецова Аналитическая геометрия Задача 6

В этой категории варианты Задачи 6, раздела "Аналитическая геометрия" в задачнике Кузнецова Л.А.

Варианты[править]

Вычислить объем тетраэдра с вершинами в точках ${\displaystyle A_{1},\ A_{2},\ A_{3},\ A_{4}}$ и его высоту, опущенную из вершины ${\displaystyle A_{4}}$ на грань ${\displaystyle A_{1}A_{2}A_{3}}$.

Задача	Условие
6-1	${\displaystyle A_{1}(1;\ 3;\ 6)}$	${\displaystyle A_{2}(2;\ 2;\ 1)}$	${\displaystyle A_{3}(-1;\ 0;\ 1)}$	${\displaystyle A_{4}(-4;\ 6;\ -3)}$
6-2	${\displaystyle A_{1}(-4;\ 2;\ 6)}$	${\displaystyle A_{2}(2;\ -3;\ 0)}$	${\displaystyle A_{3}(-10;\ 5;\ 8)}$	${\displaystyle A_{4}(-5;\ 2;\ -4)}$
6-3	${\displaystyle A_{1}(7;\ 2;\ 4)}$	${\displaystyle A_{2}(7;\ -1;\ -2)}$	${\displaystyle A_{3}(3;\ 3;\ 1)}$	${\displaystyle A_{4}(-4;\ 2;\ 1)}$
6-4	${\displaystyle A_{1}(2;\ 1;\ 4)}$	${\displaystyle A_{2}(-1;\ 5;\ -2)}$	${\displaystyle A_{3}(-7;\ -3;\ 2)}$	${\displaystyle A_{4}(-6;\ -3;\ 6)}$
6-5	${\displaystyle A_{1}(-1;\ -5;\ 2)}$	${\displaystyle A_{2}(-6;\ 0;\ -3)}$	${\displaystyle A_{3}(3;\ 6;\ -3)}$	${\displaystyle A_{4}(-10;\ 6;\ 7)}$
6-6	${\displaystyle A_{1}(0;\ -1;\ -1)}$	${\displaystyle A_{2}(-2;\ 3;\ 5)}$	${\displaystyle A_{3}(1;\ -5;\ -9)}$	${\displaystyle A_{4}(-1;\ -6;\ 3)}$
6-7	${\displaystyle A_{1}(5;\ 2;\ 0)}$	${\displaystyle A_{2}(2;\ 5;\ 0)}$	${\displaystyle A_{3}(1;\ 2;\ 4)}$	${\displaystyle A_{4}(-1;\ 1;\ 1)}$
6-8	${\displaystyle A_{1}(2;\ -1;\ -2)}$	${\displaystyle A_{2}(1;\ 2;\ 1)}$	${\displaystyle A_{3}(5;\ 0;\ -6)}$	${\displaystyle A_{4}(-10;\ 9;\ -7)}$
6-9	${\displaystyle A_{1}(-2;\ 0;\ -4)}$	${\displaystyle A_{2}(-1;\ 7;\ 1)}$	${\displaystyle A_{3}(4;\ -8;\ -4)}$	${\displaystyle A_{4}(1;\ -4;\ 6)}$
6-10	${\displaystyle A_{1}(14;\ 4;\ 5)}$	${\displaystyle A_{2}(-5;\ -3;\ 2)}$	${\displaystyle A_{3}(-2;\ -6;\ -3)}$	${\displaystyle A_{4}(-2;\ 2;\ -1)}$
6-11	${\displaystyle A_{1}(1;\ 2;\ 0)}$	${\displaystyle A_{2}(3;\ 0;\ -3)}$	${\displaystyle A_{3}(5;\ 2;\ 6)}$	${\displaystyle A_{4}(8;\ 4;\ -9)}$
6-12	${\displaystyle A_{1}(2;\ -1;\ 2)}$	${\displaystyle A_{2}(1;\ 2;\ -1)}$	${\displaystyle A_{3}(3;\ 2;\ 1)}$	${\displaystyle A_{4}(-4;\ 2;\ 5)}$
6-13	${\displaystyle A_{1}(1;\ 1;\ 2)}$	${\displaystyle A_{2}(-1;\ 1;\ 3)}$	${\displaystyle A_{3}(2;\ -2;\ 4)}$	${\displaystyle A_{4}(-1;\ 0;\ -2)}$
6-14	${\displaystyle A_{1}(2;\ 3;\ 1)}$	${\displaystyle A_{2}(4;\ 1;\ -2)}$	${\displaystyle A_{3}(6;\ 3;\ 7)}$	${\displaystyle A_{4}(7;\ 5;\ -3)}$
6-15	${\displaystyle A_{1}(1;\ 1;\ -1)}$	${\displaystyle A_{2}(2;\ 3;\ 1)}$	${\displaystyle A_{3}(3;\ 2;\ 1)}$	${\displaystyle A_{4}(5;\ 9;\ -8)}$
6-16	${\displaystyle A_{1}(1;\ 5;\ -7)}$	${\displaystyle A_{2}(-3;\ 6;\ 3)}$	${\displaystyle A_{3}(-2;\ 7;\ 3)}$	${\displaystyle A_{4}(-4;\ 8;\ -12)}$
6-17	${\displaystyle A_{1}(-3;\ 4;\ -7)}$	${\displaystyle A_{2}(1;\ 5;\ -4)}$	${\displaystyle A_{3}(-5;\ -2;\ 0)}$	${\displaystyle A_{4}(2;\ 5;\ 4)}$
6-18	${\displaystyle A_{1}(-1;\ 2;\ -3)}$	${\displaystyle A_{2}(4;\ -1;\ 0)}$	${\displaystyle A_{3}(2;\ 1;\ -2)}$	${\displaystyle A_{4}(3;\ 4;\ 5)}$
6-19	${\displaystyle A_{1}(4;\ -1;\ 3)}$	${\displaystyle A_{2}(-2;\ 1;\ 0)}$	${\displaystyle A_{3}(0;\ -5;\ 1)}$	${\displaystyle A_{4}(3;\ 2;\ -6)}$
6-20	${\displaystyle A_{1}(1;\ -1;\ 1)}$	${\displaystyle A_{2}(-2;\ 0;\ 3)}$	${\displaystyle A_{3}(2;\ 1;\ -1)}$	${\displaystyle A_{4}(2;\ -2;\ -4)}$
6-21	${\displaystyle A_{1}(1;\ 2;\ 0)}$	${\displaystyle A_{2}(1;\ -1;\ 2)}$	${\displaystyle A_{3}(0;\ 1;\ -1)}$	${\displaystyle A_{4}(-3;\ 0;\ 1)}$
6-22	${\displaystyle A_{1}(1;\ 0;\ 2)}$	${\displaystyle A_{2}(1;\ 2;\ -1)}$	${\displaystyle A_{3}(2;\ -2;\ 1)}$	${\displaystyle A_{4}(2;\ 1;\ 0)}$
6-23	${\displaystyle A_{1}(1;\ 2;\ -3)}$	${\displaystyle A_{2}(1;\ 0;\ 1)}$	${\displaystyle A_{3}(-2;\ -1;\ 6)}$	${\displaystyle A_{4}(0;\ -5;\ -4)}$
6-24	${\displaystyle A_{1}(3;\ 10;\ -1)}$	${\displaystyle A_{2}(-2;\ 3;\ -5)}$	${\displaystyle A_{3}(-6;\ 0;\ -3)}$	${\displaystyle A_{4}(1;\ -1;\ 2)}$
6-25	${\displaystyle A_{1}(-1;\ 2;\ 4)}$	${\displaystyle A_{2}(-1;\ -2;\ -4)}$	${\displaystyle A_{3}(3;\ 0;\ -1)}$	${\displaystyle A_{4}(7;\ -3;\ 1)}$
6-26	${\displaystyle A_{1}(0;\ -3;\ 1)}$	${\displaystyle A_{2}(-4;\ 1;\ 2)}$	${\displaystyle A_{3}(2;\ -1;\ 5)}$	${\displaystyle A_{4}(3;\ 1;\ -4)}$
6-27	${\displaystyle A_{1}(1;\ 3;\ 0)}$	${\displaystyle A_{2}(4;\ -1;\ 2)}$	${\displaystyle A_{3}(3;\ 0;\ 1)}$	${\displaystyle A_{4}(-4;\ 3;\ 5)}$
6-28	${\displaystyle A_{1}(-2;\ -1;\ -1)}$	${\displaystyle A_{2}(0;\ 3;\ 2)}$	${\displaystyle A_{3}(3;\ 1;\ -4)}$	${\displaystyle A_{4}(-4;\ 7;\ 3)}$
6-29	${\displaystyle A_{1}(-3;\ -5;\ 6)}$	${\displaystyle A_{2}(2;\ 1;\ -4)}$	${\displaystyle A_{3}(0;\ -3;\ -1)}$	${\displaystyle A_{4}(-5;\ 2;\ -8)}$
6-30	${\displaystyle A_{1}(2;\ -4;\ -3)}$	${\displaystyle A_{2}(5;\ -6;\ 0)}$	${\displaystyle A_{3}(-1;\ 3;\ -3)}$	${\displaystyle A_{4}(-10;\ -8;\ 7)}$
6-31	${\displaystyle A_{1}(1;\ -1;\ 2)}$	${\displaystyle A_{2}(2;\ 1;\ 2)}$	${\displaystyle A_{3}(1;\ 1;\ 4)}$	${\displaystyle A_{4}(6;\ -3;\ 8)}$