Vectors

(the database of solved problems)

All the problems and solutions shown below were generated using the Vectors Calculator.

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ID	Problem	Count
1	Calculate the cross product of the vectors $v_{1} = (4, 2, - \frac{3}{2})$ and $v_{2} = (\frac{1}{2}, 0, 2)$ .	734
2	Calculate the dot product of the vectors $v_{1} = (\frac{1}{2}, 3, 5)$ and $v_{2} = (4, - 3, 10)$ .	373
3	Find the angle between vectors $(2, 1, - 4)$ and $(3, - 5, 2)$ .	182
4	Find the magnitude of the vector $∥ v ∥ = (\frac{2}{3}, 3, 2)$ .	167
5	Find the magnitude of the vector $∥ v ∥ = (0, 0)$ .	58
6	Calculate the dot product of the vectors $v_{1} = (0, 0)$ and $v_{2} = (0, 0)$ .	41
7	Find the magnitude of the vector $∥ v ∥ = (0, 0)$ .	34
8	Find the difference of the vectors $v_{1} = (0, 0)$ and $v_{2} = (0, 0)$ .	28
9	Find the sum of the vectors $v_{1} = (0, 0)$ and $v_{2} = (0, 0)$ .	20
10	Find the projection of the vector $v_{1} = (3, 2)$ on the vector $v_{2} = (5, - 5)$ .	17
11	Find the projection of the vector $v_{1} = (0, 0)$ on the vector $v_{2} = (0, 0)$ .	14
12	Find the magnitude of the vector $∥ v ∥ = (2, 4)$ .	13
13	Find the sum of the vectors $v_{1} = (- 2, 4)$ and $v_{2} = (- 25, - 10)$ .	12
14	Find the magnitude of the vector $∥ v ∥ = (\frac{5}{3}, - \frac{3}{2})$ .	11
15	Calculate the dot product of the vectors $v_{1} = (5, - 1)$ and $v_{2} = (3, 1)$ .	10
16	Calculate the dot product of the vectors $v_{1} = (1, 2)$ and $v_{2} = (3, 4)$ .	9
17	Find the sum of the vectors $v_{1} = (4, 3)$ and $v_{2} = (2, 3)$ .	9
18	Find the magnitude of the vector $∥ v ∥ = (3, - 4)$ .	9
19	Find the sum of the vectors $v_{1} = (1, 2)$ and $v_{2} = (3, 4)$ .	8
20	Find the magnitude of the vector $∥ v ∥ = (2, - 4)$ .	8
21	Find the magnitude of the vector $∥ v ∥ = (0, 0, 0)$ .	8
22	Find the magnitude of the vector $∥ v ∥ = (11, 54)$ .	8
23	Calculate the cross product of the vectors $v_{1} = (- 2, - 1, 2)$ and $v_{2} = (1, - \frac{9}{2}, 1)$ .	8
24	Find the difference of the vectors $v_{1} = (- 6, 6)$ and $v_{2} = (- 8, 7)$ .	8
25	Calculate the dot product of the vectors $v_{1} = (4, 3)$ and $v_{2} = (2, 3)$ .	8
26	Find the magnitude of the vector $∥ v ∥ = (3, 4)$ .	7
27	Calculate the dot product of the vectors $v_{1} = (\frac{3}{2}, \frac{1}{2})$ and $v_{2} = (- \frac{2}{2}, - \frac{2}{2})$ .	7
28	Calculate the cross product of the vectors $v_{1} = (- 3, 8, - 2)$ and $v_{2} = (- 3, 7, 3)$ .	7
29	Calculate the dot product of the vectors $v_{1} = (\frac{39}{10}, \frac{23}{20})$ and $v_{2} = (0, 0)$ .	7
30	Find the sum of the vectors $v_{1} = (6, 4)$ and $v_{2} = (7, - 2)$ .	7
31	Determine whether the vectors $v_{1} = (0, 0)$ and $v_{2} = (0, 0)$ are linearly independent or dependent.	6
32	Find the magnitude of the vector $∥ v ∥ = (2, 0)$ .	6
33	Find the magnitude of the vector $∥ v ∥ = (3, - 2)$ .	6
34	Find the magnitude of the vector $∥ v ∥ = (3, 2)$ .	6
35	Find the difference of the vectors $v_{1} = (9, 6)$ and $v_{2} = (\frac{609}{65}, \frac{348}{65})$ .	6
36	Find the sum of the vectors $v_{1} = (2, 0)$ and $v_{2} = (1, 1)$ .	6
37	Find the magnitude of the vector $∥ v ∥ = (3, 5)$ .	6
38	Find the sum of the vectors $v_{1} = (1, 2, 3)$ and $v_{2} = (2, 5, 8)$ .	6
39	Find the magnitude of the vector $∥ v ∥ = (0, 0)$ .	6
40	Find the projection of the vector $v_{1} = (- 4, 3)$ on the vector $v_{2} = (5, 12)$ .	6
41	Find the difference of the vectors $v_{1} = (4, 6)$ and $v_{2} = (5, 2)$ .	6
42	Find the magnitude of the vector $∥ v ∥ = (3, 8)$ .	6
43	Find the projection of the vector $v_{1} = (1, - 3)$ on the vector $v_{2} = (5, \frac{1}{2})$ .	6
44	Find the sum of the vectors $v_{1} = (2, - 1)$ and $v_{2} = (- 1, 3)$ .	5
45	Find the sum of the vectors $v_{1} = (- \frac{2}{5}, \frac{3}{5})$ and $v_{2} = (5, 29)$ .	5
46	Calculate the dot product of the vectors $v_{1} = (\frac{70707}{1000}, \frac{16853}{200})$ and $v_{2} = (- \frac{28191}{500}, \frac{20521}{1000})$ .	5
47	Find the magnitude of the vector $∥ v ∥ = (5, 3)$ .	5
48	Calculate the dot product of the vectors $v_{1} = (5, - 9)$ and $v_{2} = (- 1, - 4)$ .	5
49	Find the projection of the vector $v_{1} = (2, - 6)$ on the vector $v_{2} = (- \frac{1}{3}, \frac{3}{5})$ .	5
50	Find the difference of the vectors $v_{1} = (\frac{3}{4}, 2)$ and $v_{2} = (3, - 2)$ .	5