Категория:Задачник Кузнецова Аналитическая геометрия Задача 3

В этой категории варианты Задачи 3, раздела «Аналитическая геометрия» в задачнике Кузнецова Л.А.

Варианты[править]

Найти косинус угла между векторами ${\displaystyle {\vec {AB}}}$ и ${\displaystyle {\vec {AC}}}$.

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