Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
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) $ . | 198 |
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) $ . | 82 |
3 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ . | 74 |
4 | Find the angle between vectors $ \left(2,~1,~-4\right)$ and $\left(3,~-5,~2\right)$. | 62 |
5 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 26 |
6 | Find the projection of the vector $ \vec{v_1} = \left(3,~2\right) $ on the vector $ \vec{v_2} = \left(5,~-5\right) $. | 17 |
7 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 17 |
8 | Find the difference of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 16 |
9 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-25,~-10\right) $ . | 12 |
10 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 11 |
11 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 5 }{ 3 },~-\dfrac{ 3 }{ 2 }\right) $ . | 11 |
12 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4\right) $ . | 10 |
13 | | 9 |
14 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 8 |
15 | 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 |
16 | Find the sum of the vectors $ \vec{v_1} = \left(6,~4\right) $ and $ \vec{v_2} = \left(7,~-2\right) $ . | 7 |
17 | 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 |
18 | 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 |
19 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 7 |
20 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 6 |
21 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 6 |
22 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~4\right) $ . | 5 |
23 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~9\right) $ . | 5 |
24 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~4\right) $ . | 5 |
25 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 5 |
26 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-9\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ . | 5 |
27 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 5 |
28 | Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(10,~5\right) $. | 5 |
29 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~5,~8\right) $ . | 5 |
30 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2\right) $ . | 5 |
31 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 5 |
32 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ . | 5 |
33 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 5 |
34 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 5 |
35 | 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 |
36 | 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 |
37 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0\right) $ . | 5 |
38 | Find the difference of the vectors $ \vec{v_1} = \left(4,~6\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 5 |
39 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 5 |
40 | 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 |
41 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(4,~5,~6\right) $ . | 5 |
42 | Find the projection of the vector $ \vec{v_1} = \left(8,~5\right) $ on the vector $ \vec{v_2} = \left(-9,~-2\right) $. | 4 |
43 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0.8,~0.2\right) $ and $ \vec{v_2} = \left(0.35,~0.65\right) $ . | 4 |
44 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~0\right) $ . | 4 |
45 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~7\right) $ . | 4 |
46 | Determine whether the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ are linearly independent or dependent. | 4 |
47 | Find the projection of the vector $ \vec{v_1} = \left(3,~-5\right) $ on the vector $ \vec{v_2} = \left(0,~1\right) $. | 4 |
48 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 4 |
49 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 4 |
50 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(8,~-2\right) $ . | 4 |