заочникам / векторная алгебра / vector

Задача 10

Найти работу силы F на пути ABC,			если:
N	F	A		B	C
1	F (3,−2,1)	A(0,−1,3)		B(1,−4,2)	C(3,1,0)
2	F (−2,0,4)	A(3,−2,5)		B(0,−1,3)	C(2,−5,6)
3	F (3,2,−1)	A(4,5,0)		B(3,1,2)	C(0,6,1)
4	F (2,−5,3)	A(4,0,−3)		B(2,1,0)	C(5,2,−4)
5	F (2,3,−4)	A(4,1,0)		B(3,−2,1)	C(0,−2,3)
6	F (3,4,−2)	A(5,0,−4)		B(4,1,2)	C(3,−2,5)
7	F (4,−3,1)	A(4,5,−2)		B(6,0,−3)	C(3,−2,1)
8	F (2,−3,5)	A(6,3,−2)		B(4,−2,1)	C(0,1,3)
9	F (3,−2,1)	A(4,1,0)		B(0,4,−3)	C(3,−2,5)
10	F (4,2,−3)	A(4,1,3)		B(2,−3,1)	C(5,0,−2)
11	F (3,2,−1)	A(4,−1,1)		B(3,0,−2)	C(4,1,−3)
12	F (4,2,−5)	A(4,4,−2)		B(4,5,−6)	C(6,0,5)
13	F (5,1,0)	A(5,1,3)		B(−3,1,6)	C(7,2,4)
14	F (3,−2,6)	A(0,−2,4)		B(3,1,2)	C(4,3,4)
15	F (3,3,5)	A(2,−1,3)		B(2,4,1)	C(7,4,−2)
16	F (2,3,5)	A(0,−2,3)		B(2,3,0)	C(5,2,6)
17	F (3,−2,4)	A(4,−2,0)		B(0,2,−3)	C(5,4,3)
18	F (3,1,4)	A(3,2,−1)		B(3,1,2)	C(5,3,4)
19	F (3,4,1)	A(3,1,5)		B(2,3,−5)	C(4,6,−1)
20	F (4,−5,2)	A(3,1,4)		B(0,−1,2)	C(6,5,4)
21	F (3,1,5)	A(2,3,4)		B(3,0,2)	C(−2,1,5)
22	F (5,6,−2)	A(2,1,3)		B(−2,0,4)	C(3,−2,6)
23	F (4,−3,2)	A(3,−2,5)		B(0,1,−3)	C(−2,1,3)
24	F (0,2,−3)	A(4,3,5)		B(−2,1,3)	C(5,6,−1)
25	F (3,−2,5)	A(3,2,−1)		B(1,5,−3)	C(6,4,−2)
26	F (4,1,3)	A(3,4,−3)		B(2,0,1)	C(5,7,−2)
27	F (4,5,−2)	A(3,−4,2)		B(0,−2,1)	C(2,−1,5)
28	F (3,2,6)	A(−2,1,3)		B(3,0,1)	C(4,−2,3)
29	F (0,−3,1)	A(2,3,−2)		B(4,2,0)	C(5,7,−1)
30	F (3,−2,5)	A(2,3,−1)		B(0,1,3)	C(−1,2,4)

Задача 11

Доказать, что векторы		r	образуют базис плоскости и найти координаты вектора c в
		a, b
этом базисе.
N	a			b	c
1	a(3,−2)			b (2,3)	c(5,12)
2	a(2,3)			b (1,−3)	c(−1,12)
3	a(2,−1)			b (3,−2)	c(−5,4)
4	a(−3,−2)			b (1,4)	c(7,8)
5	a(−2,1)			b (2,3)	c(4,10)
6	a(3,5)			b (−2,4)	c(12,−2)
7	a(4,1)			b (3,−2)	c(18,−1)
8	a(5,2)			b (3,−1)	c(1,7)
9	a(2,−3)			b (1,2)	c(−3,8)
10	a(3,−2)			b (2,−1)	c(2,−2)
11	a(1,3)			b (2,−4)	c(−5,15)
12	a(2,−1)			b (4,−2)	c(−8,4)
13	a(3,−2)			b (2,−4)	c(13,−14)
14	a(2,−1)			b (4,−2)	c(8,−4)
15	a(1,3)			b (3,5)	c(−1,1)
16	a(2,−3)			b (3,1)	c(7,−5)
17	a(3,−1)			b (4,−2)	c(2,0)
18	a(4,−2)			b (3,−1)	c(6,−4)
19	a(3,−1)			b (2,−3)	c(12,−11)
20	a(−1,2)			b (2,−3)	c(−6,10)
21	a(−3,2)			b (2,−5)	c(−11,11)
22	a(1,2)			b (−2,3)	c(4,1)
23	a(−1,3)			b (2,4)	c(−5,5)
24	a(1,3)			b (2,2)	c(4,8)
25	a(2,5)			b (1,−2)	c(7,22)
26	a(2,3)			b (1,4)	c(8,17)
27	a(−1,2)			b (2,−3)	c(0,1)
28	a(−3,2)			b (−2,1)	c(−7,5)
29	a(−1,3)			b (2,−3)	c(4,−3)
30	a(1,3)			b (2,4)	c(0,2)

Задача 12

Доказать, что векторы		r r		компланарны, a	и b - неколлинеарны. Найти линейную
		a, b, c
зависимость вектора c от a и b.
N	a			b		c
1	a(2,−1,3)			b (2,−1,0)		c(6,−3,6)
2	a(1,−3,2)			b (1,2,−1)		c(4,−7,5)
3	a(−2,1,2)			b (1,2,−1)		c(−1,8,1)
4	a(−1,2,3)			b (2,−1,2)		c(−8,7,0)
5	a(3,−1,2)			b (−2,1,3)		c(11,−4,3)
6	a(1,−3,4)			b (2,−2,3)		c(−3,1,−2)
7	a(2,−2,1)			b (3,−1,2)		c(12,−8,7)
8	a(3,−1,2)			b (1,−2,3)		c(10,0,2)
9	a(4,−1,2)			b (3,−2,1)		c(5,0,3)
10	a(2,−2,1)			b (3,−1,2)		c(3,−5,1)
11	a(2,−3,1)			b (3,−2,2)		c(−5,0,−4)
12	a(3,1,−1)			b (2,3,−2)		c(−1,−5,3)
13	a(4,1,−3)			b (3,−1,−2)		c(−1,5,0)
14	a(2,−3,1)			b (3,−2,−1)		c(8,−7,−1)
15	a(3,2,−1)			b (4,3,−2)		c(1,0,1)
16	a(1,−2,3)			b (2,−1,3)		c(−2,−5,3)
17	a(3,−2,5)			b (2,−1,3)		c(5,−4,9)
18	a(1,−2,3)			b (2,−1,2)		c(2,−7,10)
19	a(2,−1,4)			b (1,−2,3)		c(4,1,6)
20	a(3,−1,4)			b (2,−2,−3)		c(8,−4,5)
21	a(2,−3,4)			b (1,−1,−3)		c(7,−9,−1)
22	a(1,−3,3)			b (2,1,−2)		c(7,−7,5)
23	a(2,−2,4)			b (1,3,−2)		c(5,7,−2)
24	a(1,−3,2)			b (2,1,−3)		c(5,−8,3)
25	a(2,−1,3)			b (1,2,−1)		c(7,4,3)
26	a(3,2,−1)			b (−1,−4,3)		c(6,−6,6)
27	a(2,1,−3)			b (3,−1,−2)		c(8,−1,−7)
28	a(1,3,−2)			b (2,1,4)		c(4,7,0)
29	a(3,2,1)			b (2,3,−1)		c(5,0,5)
30	a(4,1,−2)			b (3,2,−1)		c(9,1,−5)

Задача 13

Доказать, что векторы		r r		линейно независимы и найти координаты вектора d в базисе
		a, b, c
r	r
a, b, c.
N	a			b	c	d
1	a(1,−2,3)			b (3,−1,0)	c(2,−1,1)	d (3,−2,5)
2	a(2,−1,4)			b (1,0,2)	c(3,−2,5)	d (4,0,9)
3	a(3,−1,0)			b (4,2,3)	c(5,3,−1)	d (7,−5,8)
4	a(4,2,−1)			b (3,0,−1)	c(3,1,−2)	d (9,7,−1)
5	a(3,−2,1)			b (2,−1,0)	c(4,−2,2)	d (4,−3,0)
6	a(2,−1,3)			b (1,−2,4)	c(3,0,2)	d (1,−2,4)
7	a(3,2,−4)			b (2,1,−1)	c(1,3,−3)	d (4,1,−5)
8	a(2,−1,3)			b (3,−2,4)	c(1,−3,2)	d (1,5,1)
9	a(1,−3,2)			b (2,−1,1)	c(3,−4,2)	d (3,−9,5)
10	a(−2,1,3)			b (1,2,2)	c(−1,3,1)	d (−6,3,1)
11	a(2,3,−1)			b (1,2,0)	c(3,5,1)	d (3,6,2)
12	a(3,1,−1)			b (2,2,1)	c(4,0,3)	d (3,5,−2)
13	a(3,2,−2)			b (2,1,−3)	c(5,3,−4)	d (3,2,−3)
14	a(4,2,−1)			b (3,−1,1)	c(7,1,2)	d (5,5,−1)
15	a(1,3,−2)			b (2,1,−1)	c(2,3,−3)	d (6,6,−4)
16	a(2,0,−1)			b (1,2,−3)	c(1,2,−4)	d (6,0,−1)
17	a(3,1,−1)			b (2,2,−3)	c(5,1,−4)	d (5,5,−4)
18	a(4,−2,1)			b (3,−1,2)	c(2,0,−1)	d (3,−3,1)
19	a(3,−1,2)			b (2,−2,3)	c(5,−3,1)	d (2,−2,7)
20	a(2,4,−1)			b (1,3 − 2)	c(1,7,−3)	d (5,7,−3)
21	a(3,1,−2)			b (2,3,−1)	c(1,4,−3)	d (6,7,−9)
22	a(4,1,−2)			b (3,2,−1)	c(1,3,−3)	d (7,2,−7)
23	a(1,3,−2)			b (2,−1,1)	c(3,1,−1)	d (−7,9,−6)
24	a(2,−2,1)			b (3,−1,2)	c(5,−3,1)	d (2,−2,3)
25	a(3,−1,2)			b (2,−2,1)	c(1,−3,2)	d (3,3,1)
26	a(2,−1,3)			b (3,−2,1)	c(1,2,3)	d (−2,−2,0)
27	a(3,−2,2)			b (1,−1,2)	c(2,−1,1)	d (4,−2,1)
28	a(2,−1,1)			b (1,−2,2)	c(3,−3,1)	d (2,−1,3)
29	a(1,−2,3)			b (2,−1,2)	c(3,−3,1)	d (2,−2,6)
30	a(4,−1,2)			b (3,−2,1)	c(1,1,0)	d (6,1,3)

Задача 14

Найти составляющие h и g вектора c,				ортогональную и компланарную векторам a и b.
N	a		b		c
1	a	(2,0,1)	b (0,−1,−1)		c(5,1,−1)
2	c(3,6,1)		b (8,16,0)		c(3,1,3)
3	a(5,1,−1)		b (9,3,−1)		c(0,−1,4)
4	a(2,1,−3)		b (7,4,−10)		c(3,0,0)
5	a(3,−1,3)		b (2,0,4)		c(1,4,0)
6	a(1,−2,1)		b (0,−4,3)		c(4,3,3)
7	a(2,−3,2)		b (5,−8,4)		c(5,1,1)
8	a(2,3,−3)		b (2,5,−3)		c(5,1,−1)
9	a	(1,1,1)	b (3,3,4)		c(3,−3,1)
10	a	(1,2,−1)	b (1,4,−1)		c(5,0,−1)
11	a	(1,4,0)	b (3,10,−1)		c(5,1,1)
12	a	(1,−5,0)	b (2,−8,1)		c(6,−2,−1)
13	a	(1,2,2)	b (0,1,3)		c(5,−2,0)
14	a	(2,−1,4)	b (5,−1,13)		c(4,3,4)
15	a	(4,1,4)	b (10,1,7)		c(−1,5,−1)
16	a	(1,2,5)	b (4,4,16)		c(4,−1,0)
17	a	(3,3,−1)	b (7,8,−2)		c(4,0,2)
18	a	(4,1,−1)	b (6,2,−1)		c(3,−1,2)
19	a	(1,1,−1)	b (2,1,−4)		c(6,1,−2)
20	a	(1,0,2)	b (3,−2,5)		c(5,−1,−1)
21	a	(1,1,0)	b (0,1,3)		c(5,−2,−2)
22	a	(2,1,−1)	b (5,4,−2)		c(1,0,4)
23	a	(1,1,−2)	b (2,1,−6)		c(5,0,1)
24	a	(2,3,1)	b (4,2,2)		c(3,−1,−1)
25	a	(2,−6,0)	b (1,−5,−1)		c(4,0,−1)
26	a	(−1,−1,1)	b (0,−3,1)		c(4,0,2)
27	a	(2,2,3)	b (3,2,3)		c(1,−1,5)
28	a	(−1,1,1)	b (−1,3,4)		c(3,3,−1)
29	a	(0,3,1)	b (−1,11,3)		c(3,−1,−3)
30	a	(2,1,2)	b (3,2,4)		c(1,−1,3)

Задача 15

В параллелограмме ABCD с срединами сторон E, F , G, H и вектором M найти вершины, если даны:

N	Точки
1	E(4,−4,4), F (8,−3,2),Y (6,2,−2)
2	E(1,−5,2),Y (5,−11,2), H (3,−5,1)
3	F (7,−11,7),Y (9,−10,6), H (5,−5,5)
4	E(6,2,2), F (10,−1,7), H (8,3,1)
5	E(4,5,2), F (7,7,7), M (6,4,5)
6	F (8,−12,10), M (6,−8,7),Y (9,−10,8)
7	Y (14,−2,10), M (10,−1,7), H (8,−4,8)
8	E(5,1,−3), M (9,−2,1), H (6,0,−2)
9	E(3,3,5), F (6,4,8),Y (7,−3,7)
10	F (13,−1,4),Y (12,−2,3), H (5,1,−2)
11	E(5,4,3),Y (7,8,−3), H (3,5,−4)
12	E(5,3,7), F (8,8,15), H (6,0,5)
13	E(4,−3,3), F (7,−3,8), M (6,−2,6)
14	F (−1,3,8),Y (0,4,7), M (1,2,6)
15	Y (7,1,9), H (4,−2,4), M (6,−1,6)
16	E(5,0,4), H (4,1,3), M (6,3,6)
17	E(4,2,4), F (7,7,6),Y (6,6,6)
18	F (8,3,9),Y (7,4,8), H (4,−1,3)
19	E(6,−1,3),Y (8,5,7), H (5,5,3)
20	E(5,0,2), F (8,5,5), H (4,1,3)
21	E(6,−1,3), F (9,4,6), M (7,2,5)
22	F (2,4,6),Y (5,5,7), M (4,2,5)
23	Y (9,6,7), H (6,1,4), M (7,3,6)
24	E(5,1,5), H (4,2,3), M (6,4,6)
25	E(4,−2,1), F (7,2,6),Y (6,4,5)
26	F (8,3,9),Y (7,4,8), H (4,−1,3)
27	E(4,−3,2), G(7,1,5), H (3,−1,1)
28	E(2,4,−2), F (1,5,2), M (2,4,0)
29	E(6,6,4), H (4,3,−1), M (3,5,2)

Задача 16

Отрезок A1 A5 разделен на четыре равные части. Найти координаты остальных точек, если даны:

N	Дано		N	Дано
1	A1	(2,−1,3), A4 (5,5,−3)	16	A1	(3,−7,5), A4 (6,2,−1)
2	A2 (3,−1,2), A5 (6,5,5)		17	A2		(3,−2,3), A5 (9,7,9)
3	A1	(−4,2,1), A3 (2,4,5)	18	A1	(−8,1,5), A3 (−2,5,3)
4	A2 (3,−2,3), A4 (7,4,5)		19	A (4,0,4), A (−2,4,2)
				2		4
5	A3 (5,2,1), A5 (9,8,−1)		20	A3 (2,0,3), A5 (−2,4,5)
6	A1	(2,−3,2), A4 (5,6,−1)	21	A1	(1,5,−5), A4 (7,−1,4)
7	A2 (−2,2,1), A5 (4,5,−2)		22	A2		(−1,−4,3), A5 (2,5,−3)

8	A1 (1,−2,5), A3 (5,2,3)			23	A1 (4,1,−6), A3 (0,5,0)
9	A2 (3,−1,3), A4 (5,3,1)			24	A2 (2,2,−4), A4 (0,6,2)
10	A3	(4,0,1), A5 (6,6,−1)		25	A3	(5,3,4), A5 (1,7,6)
11	A1	(0,4,−3), A4	(6,1,3)	26	A1	(2,−5,5), A4 (5,4,−1)
12	A2 (3,−2,0), A5 (9,7,−6)			27	A2 (5,0,−3), A5 (−4,6,6)
13	A1	(2,−7,5), A3	(4,−1,3)	28	A1	(1,−7,3), A3 (5,−1,1)
14	A2 (3,−3,3), A4		(1,1,7)	29	A2 (−1,3,−4), A4 (3,5,2)
15	A3	(4,1,2), A5 (6,7,6)		30	A3	(5,−1,3), A5 (1,3,5)

Задача 17

В тетраэдре ABCD найти объем V, площадь S основания ABC,				высоту H = DK и высоту
h = CL основания.
N	A	B	C		D
1	A(−1,2,5)	B(0,4,7)	C(5,16,12)		D(0,4,22)
2	A(2,−3,1)	B(3,1,9)	C(3,−3,2)		D(4,1,19)
3	A(3,−5,4)	B(4,−3,2)	C(9,9,−3)		D(9,1,7)
4	A(4,−2,5)	B(5,2,−3)	C(5,−6,11)		D(6,−2,21)
5	A(−1,−3,−5)	B(0,−1,−3)	C(8,11,23)		D(9,13,40)
6	A(2,1,−3)	B(3,5,5)	C(6,−7,−13)		D(2,17,−2)
7	A(2,−3,1)	B(4,1,5)	C(5,−1,17)		D(4,−3,−15)
8	A(2,−1,3)	B(3,3,11)	C(5,−5,−1)		D(6,−1,16)
9	A(−2,4,3)	B(−1,6,5)	C(4,24,−5)		D(−2,26,8)
10	A(2,−3,1)	B(3,1,−7)	C(4,−3,−1)		D(4,1,10)
11	A(3,2,−1)	B(4,0,1)	C(4,−4,−9)		D(4,−6,23)
12	A(4,2,3)	B(5,0,1)	C(16,−26,−11)		D(11,−14,24)
13	A(3,−1,2)	B(4,−5,−6)	C(5,7,14)		D(5,−1,9)
14	A(3,5,−1)	B(4,1,−9)	C(7,13,9)		D(3,3,0)
15	A(−1,2,0)	B(0,0,−2)	C(8,−12,−28)		D(9,−14,−15)
16	A(2,5,9)	B(3,1,1)	C(5,9,13)		D(6,5,32)
17	A(2,3,5)	B(3,1,1)	C(5,1,−11)		D(6,−1,17)
18	A(4,3,4)	B(5,−1,12)	C(6,3,6)		D(6,−1,4)
19	A(2,3,4)	B(3,1,2)	C(5,−7,8)		D(6,−9,−9)
20	A(2,6,−1)	B(3,2,7)	C(3,10,−7)		D(4,6,28)
21	A(2,3,−6)	B(3,6,−8)	C(4,−4,10)		D(4,0,15)
22	A(−1,3,2)	B(0,−1,10)	C(3,11,−8)		D(2,3,8)
23	A(3,1,5)	B(4,3,3)	C(15,29,−9)		D(3,−2,5)
24	A(−1,4,3)	B(0,8,−5)	C(2,0,7)		D(3,4,26)
25	A(3,−1,2)	B(4,1,0)	C(12,13,−26)		D(−1,−1,0)
26	A(2,−3,2)	B(3,1,−6)	C(4,−3,0)		D(4,1,2)
27	A(3,−4,8)	B(4,−2,6)	C(6,−2,−8)		D(7,0,5)
28	A(3,−2,−1)	B(4,2,9)	C(4,−6,5)		D(5,−2,24)
29	A(−3,1,2)	B(−2,3,0)	C(0,11,6)		D(2,−3,2)
30	A(1,5,−3)	B(2,9,−11)	C(5,−3,7)		D(0,3,−3)

Задача 18

Записать формулы преобразования АСК, если дано новое начало O*							и базисные векторы
r		r	* . Найти новые координаты точки M .
e *	, e
1	2			r		r
N			O*					M
				e1*		e2*
1			(2,-1)	(1,-2)		(3,5)		(9,7)
2			(2,0)	(3,0)		(1,-2)		(12,-2)
3			(2,1)	(3,-2)		(4,-1)		(15,-6)
4			(3,1)	(2,0)		(1,3)		(7,-5)
5			(5,4)	(1,0)		(0,1)		(9,5)
6			(3,-4)	(1,-1)		(3,0)		(5,-3)
7			(3,0)	(1,-1)		(0,1)		(3,1)
8			(-1,1)	(3,-1)		(0,3)		(2,-6)
9			(3,-1)	(0,-3)		(2,0)		(1,-4)
10			(-2,2)	(1,0)		(0,-1)		(-1,1)
11			(3,-1)	(7,1)		(3,-1)		(18,4)
12			(3,4)	(2,0)		(-3,2)		(0,1)
13			(3,-1)	(0,-1)		(3,1)		(0,0)
14			(3,4)	(-1,5)		(-4,0)		(0,-1)
15			(1,-3)	(3,0)		(0,1)		(-2,0)
16			(0,0)	(3,-3)		(-2,2)		(1,-1)
17			(3,-5)	(1,0)		(0,1)		(0,0)
18			(-1,2)	(3,4)		(0,2)		(-4,0)
19			(3,0)	(3,3)		(-1,3)		(16,9)
20			(1,2)	(-1,-1)		(3,1)		(-2,-1)
21			(3,-1)	(0,3)		(3,0)		(3,-1)
22			(-1,1)	(3,4)		(0,-5)		(2,0)
23			(0,-1)	(7,3)		(3,0)		(1,2)
24			(3,1)	(1,3)		(-1,-3)		(3,1)
25			(4,-10	(2,0)		(0,-2)		(0,1)
26			(3,2)	(2,3)		(1,-1)		(2,0)
27			(3,0)	(0,3)		(-3,0)		(0,0)
28			(3,4)	(2,1)		(-1,2)		(3,4)
29			(3,-1)	(2,3)		(-1,1)		(8,9)
30			(-1,1)	(3,0)		(0,-1)		(8,1)

Задача 19

Записать формулы преобразования ДСК на плоскости при новом начале O* и угле поворота α. Найти старые координаты точки M .

N	O*	α	M *							N	O*	α	M *
1	(3,-2)	0o	(5,-1)							16	(3,-2)	330o
													(0,2				3 )
2	(-2,1)	30o	(0,1)							17	(4,-5)	0o	(1,3)
3	(0,0)	45o								18	(1,-1)	30o
			(0,			2 )							(-2				3 ,2)
4	(1,0)	60o	(2,-8)							19	(-1,3)	45o
													(	2 , 2 )
5	(2,3)	90o	(5,7)							20	(0,-1)	60o
													(	3 ,1)
6	(1,0)	120o								21	(1,2)	90o	(1,-2)
			( 3 ,-1)
7	(3,-2)	135o	(1,-1)							22	(3,-2)	120o
													(3,				3 )
8	(1,-2)	150o								23	(-1,1)	135o	(1,1)
			(2			3 ,0)
9	(4,-3)	180o	(3,5)							24	(0,1)	150o
													(-2				3 ,2)

10	(2,-3)	210o								25	(0,0)							180o	(1,1)
			(4	3 ,2)
11	(0,1)	225o								26								210o	(2,0)
			(	2 ,0)							( 3 ,- 3 )
12	(3,1)	240o								27	(1,1)							225o
			(2	3 ,2)															( 2 ,0)
13	(2,1)	270o	(2,0)							28								240o	(2,0)
											(1, 3 )
14	(3,0)	300o								29	(-3,1)							270o	(3,0)
			(2, 2 3 )
15	(4,2)	315o	(1,1)							30	(0,0)							300o
																			(2,2 3 )

Задача 20

				r
В треугольнике с данными вершинами найти координаты векторов: высоты AK , медианы
r		r
AL, биссектрисы AM .
N	A		B	C
1	(0,1,2)		(1,3,4)	(1,5,10)
2	(3,-2,1)		(4,0,3)	(5,0,2)
3	(-2,1,3)		(0,6,17)	(-1,,5)
4	(3,0,-2)		(3,3,2)	(5,5,12)
5	(-1,2,0)		(3,10,8)	(1,7,14)
6	(0,1,3)		(1,-1,5)	(1,-3,11)
7	(3,-2,1)		(4,0,-1)	(7,6,-7)
8	(4,0,-1)		(3,-2,-3)	(6,3,5)
9	(2,-1,0)		(4,-4,6)	(2,-4,-4)
10	(4,5,11)		(4,2,7)	(5,1,3)
11	(3,-5,0)		(4,-1,8)	(1,1,9)
12	(4,-3,2)		(0,5,10)	(4,2,-10)
13	(6,-2,1)		(6,-5,-3)	(4,3,15)
14	(2,0,-3)		(4,6,6)	(2,5,9)
15	(4,0,-2)		(6,3,4)	(6,6,7)
16	(5,-3,0)		(1,-11,8)	(7,2,14)
17	(6,-1,3)		(7,1,5)	(4,2,-3)
18	(-1,3,5)		(1,6,-1)	(-1,6,9)
19	(2,-2,3)		(2,1,-1)	(1,2,-5)
20	(4,0,-6)		(3,4,2)	(2,6,3)
21	(4,0,-1)		(6,6,8)	(4,5,-13)
22	(3,-2,6)		(3,3,-6)	(5,3,-8)
23	(0,-1,2)		(2,4,-12)	(1,1,0)
24	(-3,0,-2)		(-2,2,0)	(-1,3,-8)
25	(1,-2,4)		(3,1,10)	(1,1,0)
26	(3,-1,0)		(3,2,-4)	(4,3,8)
27	(-4,5,1)		(-3,1,9)	(-2,-1,10)
28	(0,-2,-5)		(2,1,1)	(0,3,7)
29	(0,-4,1)		(1,-2,3)	(1,0,-7)
30	(2,-3,5)		(3,1,-3	(4,3,-4)