Задание1.3
По координатам точек a, b и сдля указанных векторов найти:
а) модуль вектора а;
б)
скалярное произведение векторов a и
b;
в) проекцию вектора c на вектор d;
г)
координаты точки M, делящей отрезок lв отношении
.
1.
A (4, 6, 3), B (-5, 2, 6), C (4, -4, -3), a = 
-
,
b =
,
c = 
,
d = 
,
l = AB, 
= 5, 
= 4.
2.
A (4, 3, -2), B (-3, -1, 4), C (2, 2, 1), a = 
,
b = 
,
c = 
,
d = 
,
l = BC, 
= 2, 
= 3.
3.
A (-2, -2, 4), B (1, 3, -2), C (1, 4, 2), a =
,
b =
,
c =
,
d =
,
l = BA, 
=2, 
=1.
4.
A (2, 4, 3), B (3, 1, -4), C (-1, 2, 2), a =
+
,
b =
,
c = b, d = 
,
l = BA, 
= 1, 
= 4.
5.
A (2, 4, 5), B (1, -2, 3), C (-1, -2, 4), a =
,
b =
,
c = b, d =
,
l = AB, 
= 2, 
= 3.
6.
A (-1, -2, 4), B (-1, 3, 5), C (1, 4, 2), a =
,
c = b = 
,
d =
,
l = AC, 
= 1, 
= 7.
7.
A (1, 3, 2), B (2, 4, 1), C (1, 3, 2), a =
+
,
B =
,с
= b, d =
,
l = AB,
= 2,
= 4.
8.
A (2, -4, 3), B (-3, -2, 4), C (0, 0, -2), a =
-
,
b = c =
,
d =
,
l = AC, 
= 2,
= 1.
9.
A (3, 4, -4), B (-2, 1, 2), C (2, -3, 1), a = 
-
,
b = c =
,
d =
,
l = AB, 
= 2, 
= 5.
10.
A (0, 2, 5), B (2, -3, 4), C (3, 2, -5), a =
+
,
b = c =
,
d =
,
l = AC, 
= 3, 
= 2.
11.
A (-2,-3, -4), B (2, -4, 0), C (1, 4, 5), a =
-
,
b = c =
,
d=
,
l =AB, 
= 4, 
= 2.
12.
A (-2, -3, -2), B (1, 4, 2), C (1, -3, 3), a =
-
,
b = c=
,
d =
,
l = BC, 
= 3, 
=
1.
13.
A (5, 6, 1), B (-2, 4,-1), C (3,-3,3), a =
-
,
b = c =
,
d =
,
l = BC, 
= 3, 
=
2.
14.
A (10, 6, 3), B (-2, 4, 5), C (3, -4, -6), a = 
-
,
b = c= 
,
d = 
,
l = AC, 
= 2, 
= 4.
15.
A (3, 2, 4), B (-2, 1, 3), C (2, -2, -1), a = 
-
,
b = 
,
c = 
,
d = 
,
l = AB, 
= 2, 
= 5.
16.
A (-2, 3, -4), B (3, -1, 2), C (4, 2, 4), a = 
+
,
b = c = 
,
d = 
,
l = BC, 
= 2, 
= 5.
17.
A (4, 5, 3), B (-4, 2, 3), C (5, -6, -2), a = 
-
,
b = c= 
,
d = 
,
l = BC, 
= 5, 
= 1.
18.
A (2, 4, 6), B (-3, 5, 1), C (4, -5, -4), a = 
+
,
b = c = 
,
d = 
,
l = BC, 
= 1, 
= 3.
19.
A (-4, -2, -5), B (3, 7, 2), C (4, 6, -3), a = 
+
,
b = c = 
,
d = 
,
l = BA, 
= 4, 
= 3.
20.
A (5, 4, 4), B (-5, 2, 3), C (4, 2, -5), a =
-
,
b =
,
c =
,
d = 
,
l = BC, 
=
3, 
= 1.
21.
A (3, 4, 6), B (-4, 6, 4), C (5, -2, -3), a = 
+
,
b = 
,
c = 
,
d = 
,
l = BA, 
= 5, 
= 3.
22.
A (-5, -2, -6), B (3, 4, 5), C (2, -5, 4), a = 
-
,
b = c = 
,
d = 
,
l = AC, 
= 3, 
= 4.
23.
A (3, 4, 1), B (5, -2, 6), C (4, 2, -7), a = 
+
,
b = c = 
,
d = 
,
l = AB, 
= 2, 
= 3.
24.
A (4, 3, 2), B (-4, -3, 5), C (6, 4, -3), a = 
-
,
b = c = 
,
d = 
,
l = BC, 
= 2, 
= 5.
25.
A (-5, 4, 3), B (4, 5, 2), C (2, 7, -4), a = 
+
,
b = c = 
,
d = 
,
l = BC, 
= 3, 
= 4.
26.
A (6, 4, 5), B (-7, 1, 8), C (2, -2, -7), a = 
-
,
b = 
,
c = 
,
d = 
,
l = AB, 
= 3, 
= 2.
27.
A (6, 5, -4), B (-5, -2, 2), C (3, -3, 2), a = 
-
,
b = c = 
,
d = 
,
l = BC, 
= 1, 
= 5.
28.
A (-3, -5, 6), B (3, 5, -4), C (2, 6, 4), a = 
-
,
b = 
,
c = 
,
d = 
,
l = BA, 
= 4, 
= 2.
29.
A (3, 5, 4), B (4, 2, -3), C (-2, 4, 7), a = 
-
,
b = 
,c
= 
d = 
,
l = BA, 
= 2, 
= 5.
30.
A (4, 6, 7), B (2, -4, 1), C (-3, -4, 2), a = 
-
,
b = c = 
,
d = 
,
l = AB, 
= 3, 
= 4.