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Lesson 1: Three-Dimensional Cartesian Coordinates and Vector Operations — Picture questions (exam style)

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1.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
14.97
7.483
3.5
8.261
2.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
46.23
-11
-77
77
3.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
19
7.228
20.33
14.46
4.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
21.21
19.21
38.42
9
5.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
14
53
15
-53
6.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
40.25
150
-150
-30
7.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-6
14.49
6
2
8.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-56
56
64.51
-10
9.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-22
6
-6
41.83
10.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
31.4
29
15.7
32.98
11.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
24
69.57
34.79
42.26
12.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-3
-1
1
48.83
13.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
9.028
2
18.06
9.247
14.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
29
38.79
14
-29
15.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
57.25
0
-3
3
16.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
54
-54
12.73
-1
17.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
6
27
-36
-6
18.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
13.86
18.33
27.71
12
19.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
32.65
-3
28
-28
20.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
25.17
26.41
50.34
8
21.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
36.88
73.32
4
36.66
22.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
45.87
-19
9
19
23.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-10
41.11
-26
26
24.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
34
32.94
65.88
47.34
25.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
26
32.7
16.35
30.71
26.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
12
50.7
28.04
25.35
27.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
8.078
7.5
15
3
28.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-90
90
-45
43.59
29.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-94
20.1
-6
94
30.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-53
-3
37.54
53
31.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
57.45
-10
10
6
32.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
25
-8
41.23
8
33.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
19.47
4.5
10.72
9.734
34.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
44.93
-25
-29
29
35.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-71
71
98.51
-3
36.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
35.9
-6
6
4
37.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-19
19
33
6.708
38.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
3
22.05
22.25
44.09
39.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-56
43.15
56
8
40.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
90.75
-11
-35
35
41.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
30.51
22.6
20.5
45.2
42.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
16.16
5
16.91
32.31
43.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
17
45.3
41.99
83.98
44.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
6
33.61
67.22
34.14
45.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
2.5
15.33
8.062
7.665
46.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-21
21
24.74
19
47.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-16
90
48.56
-90
48.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-15
15
53.24
12
49.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
3.742
28
28.06
1.871
50.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
19.34
30
38.68
35.69
51.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
20.45
35.67
17.83
10
52.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
13
-13
-6
19.42
53.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
10
90
-90
69.32
54.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-54
27.93
-4
54
55.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
19.5
21.11
16.16
8.078
56.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
31
40.3
80.6
50.84
57.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-24
28.28
24
6
58.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
37.99
75.97
39
54.44
59.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
49.5
0
25
1
60.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-23
40.02
23
12.08
61.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
12
4
12.65
8
62.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-90
90
-32
76.16
63.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-11
11
28.14
12
64.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
12.73
6.364
32.5
33.12
65.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-6
40.99
10.44
6
66.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
85.85
27
-27
-15
67.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
43.96
45.99
13.5
87.93
68.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
26.05
52.1
27.25
8
69.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
7.071
3.536
26.24
26
70.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
30
6
14.07
-6
71.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
18.5
28.65
23.4
14.33
72.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-2
-38
50.58
38
73.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-11
16
-16
43.75
74.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
40
44.02
36.77
18.38
75.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-23
20
14.46
23
76.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
26.42
52.84
2
26.5
77.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-1
39.76
-83
83
78.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
62.64
-9
9
-2
79.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
81.82
-70
70
12
80.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
7
25.42
72
-72
81.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
31.12
5
30.72
61.43
82.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
9.682
18.06
3.5
9.028
83.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
24.92
11
44.72
22.36
84.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
46.95
16.37
44
32.74
85.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
28.53
2
14.27
14.4
86.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
45
43.43
86.86
62.54
87.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
14.9
10.22
7
7.45
88.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
19.5
23.48
46.96
30.52
89.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
0
26
-26
39.45
90.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
38.42
20.12
6
19.21
91.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
33.23
18
16.61
24.49
92.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
12
33.97
31.78
63.57
93.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
30.89
15.44
13.5
20.51
94.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
28.43
14.21
11
17.97
95.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
45.5
48.79
35.24
17.62
96.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
11.51
9.5
13
6.5
97.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
31.11
16
-16
-9
98.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-3
1
115
0
99.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
2
18.04
17.93
35.86
100.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-24
47.22
-7
24
101.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
30.81
31.07
61.62
4
102.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-1
11
-11
13.15
103.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
40.47
-98
-35
98
104.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
17.72
21
6
-6
105.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
62.86
58.88
22
117.8
106.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
12.5
30.31
55.23
27.61
107.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-16
16
18.14
9
108.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
32.45
17.87
7.5
16.22
109.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
58.74
39.5
43.48
86.96
110.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
38.64
27.1
19.32
19
111.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
39
27
-4
-39
112.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
41.02
76.37
15
38.18
113.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
16.02
10.61
12
21.21
114.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
41.32
10.5
79.94
39.97
115.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
13.5
12.83
18.62
25.65
116.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
59.67
72
-72
-34
117.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
47.57
44.68
42
22.34
118.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-7
22.91
7
-1
119.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
4
57.5
-3
3
120.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
16
-5
-16
28.28
121.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
37.42
18.71
42.5
46.44
122.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
63.16
56
29.21
58.43
123.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
26.5
52
-52
-10
124.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
32.76
65.52
4.5
33.07
125.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
84.43
-50
50
-2
126.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
8
21
-8
28
127.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-2
85
39.57
-85
128.
Find the area of triangle ABC (use the vector product).
Find the area of triangle ABC (use the vector product).
12.5
6.225
12.45
13.96
129.
Find the scalar product AB · AC.
Find the scalar product AB · AC.
-7
8
9.274
7
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