Vectors – Solved Problems Database

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 $ \vec{v_1} = \left(4,~2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~0,~2\right) $ .	734
2	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\sqrt{ 3 },~5\right) $ and $ \vec{v_2} = \left(4,~-\sqrt{ 3 },~10\right) $ .	373
3	Find the angle between vectors $ \left(2,~1,~-4\right)$ and $\left(3,~-5,~2\right)$.	182
4	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ .	167
5	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	58
6	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	41
7	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	34
8	Find the difference of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	28
9	Find the sum of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	20
10	Find the projection of the vector $ \vec{v_1} = \left(3,~2\right) $ on the vector $ \vec{v_2} = \left(5,~-5\right) $.	17
11	Find the projection of the vector $ \vec{v_1} = \left(0,~0\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $.	14
12	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~4\right) $ .	13
13	Find the sum of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-25,~-10\right) $ .	12
14	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 5 }{ 3 },~-\dfrac{ 3 }{ 2 }\right) $ .	11
15	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(3,~1\right) $ .	10
16		10
17	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-4\right) $ .	9
18	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ .	9
19	Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(2,~3\right) $ .	9
20	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(11,~54\right) $ .	8
21	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-4\right) $ .	8
22	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(2,~3\right) $ .	8
23	Find the difference of the vectors $ \vec{v_1} = \left(-6,~6\right) $ and $ \vec{v_2} = \left(-8,~7\right) $ .	8
24	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0,~0\right) $ .	8
25	Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-1,~2\right) $ and $ \vec{v_2} = \left(1,~-\dfrac{ 9 }{ 2 },~1\right) $ .	8
26	Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ .	8
27	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{\sqrt{ 3 }}{ 2 },~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(- \dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right) $ .	7
28	Find the sum of the vectors $ \vec{v_1} = \left(6,~4\right) $ and $ \vec{v_2} = \left(7,~-2\right) $ .	7
29	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~4\right) $ .	7
30	Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~-2\right) $ and $ \vec{v_2} = \left(-3,~7,~3\right) $ .	7
31	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 39 }{ 10 },~\dfrac{ 23 }{ 20 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	7
32	Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~5,~8\right) $ .	6
33	Determine whether the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ are linearly independent or dependent.	6
34	Find the projection of the vector $ \vec{v_1} = \left(1,~-3\right) $ on the vector $ \vec{v_2} = \left(5,~\dfrac{ 1 }{ 2 }\right) $.	6
35	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~0\right) $ .	6
36	Find the difference of the vectors $ \vec{v_1} = \left(4,~6\right) $ and $ \vec{v_2} = \left(5,~2\right) $ .	6
37	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~8\right) $ .	6
38	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~2\right) $ .	6
39	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~5\right) $ .	6
40	Find the projection of the vector $ \vec{v_1} = \left(-4,~3\right) $ on the vector $ \vec{v_2} = \left(5,~12\right) $.	6
41	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-2\right) $ .	6
42	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	6
43	Find the difference of the vectors $ \vec{v_1} = \left(9,~6\right) $ and $ \vec{v_2} = \left(\dfrac{ 609 }{ 65 },~\dfrac{ 348 }{ 65 }\right) $ .	6
44	Find the sum of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ .	6
45	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 70707 }{ 1000 },~\dfrac{ 16853 }{ 200 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 28191 }{ 500 },~\dfrac{ 20521 }{ 1000 }\right) $ .	5
46	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-9\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ .	5
47	Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(5,~29\right) $ .	5
48	Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 4 },~2\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ .	5
49	Find the projection of the vector $ \vec{v_1} = \left(2,~-6\right) $ on the vector $ \vec{v_2} = \left(-\dfrac{ 1 }{ 3 },~\dfrac{ 3 }{ 5 }\right) $.	5
50	Find the sum of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ .	5