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) $ . | 144 |
2 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ . | 64 |
3 | 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) $ . | 58 |
4 | Find the angle between vectors $ \left(2,~1,~-4\right)$ and $\left(3,~-5,~2\right)$. | 45 |
5 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 17 |
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 sum of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-25,~-10\right) $ . | 12 |
8 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 5 }{ 3 },~-\dfrac{ 3 }{ 2 }\right) $ . | 11 |
9 | Find the difference of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 11 |
10 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4\right) $ . | 10 |
11 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 9 |
12 | | 9 |
13 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 9 |
14 | 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 |
15 | Find the sum of the vectors $ \vec{v_1} = \left(6,~4\right) $ and $ \vec{v_2} = \left(7,~-2\right) $ . | 7 |
16 | 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 |
17 | 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 |
18 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 7 |
19 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 6 |
20 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~4\right) $ . | 5 |
21 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~9\right) $ . | 5 |
22 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 5 |
23 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-9\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ . | 5 |
24 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 5 |
25 | Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(10,~5\right) $. | 5 |
26 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~5,~8\right) $ . | 5 |
27 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2\right) $ . | 5 |
28 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ . | 5 |
29 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 5 |
30 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 5 |
31 | 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 |
32 | 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 |
33 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0\right) $ . | 5 |
34 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 5 |
35 | 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 |
36 | 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 |
37 | Find the projection of the vector $ \vec{v_1} = \left(8,~5\right) $ on the vector $ \vec{v_2} = \left(-9,~-2\right) $. | 4 |
38 | 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 |
39 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~0\right) $ . | 4 |
40 | Find the projection of the vector $ \vec{v_1} = \left(3,~-5\right) $ on the vector $ \vec{v_2} = \left(0,~1\right) $. | 4 |
41 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 4 |
42 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 4 |
43 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(8,~-2\right) $ . | 4 |
44 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 29 }{ 10 },~\dfrac{ 307 }{ 100 }\right) $ and $ \vec{v_2} = \left(240,~300\right) $ . | 4 |
45 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~8\right) $ and $ \vec{v_2} = \left(-9,~2\right) $ . | 4 |
46 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~0\right) $ . | 4 |
47 | Find the angle between vectors $ \left(-6,~3\right)$ and $\left(7,~-1\right)$. | 4 |
48 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~7\right) $ . | 4 |
49 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-1\right) $ and $ \vec{v_2} = \left(5,~7\right) $ . | 4 |
50 | Calculate the dot product of the vectors $ \vec{v_1} = \left(11,~1\right) $ and $ \vec{v_2} = \left(1,~11\right) $ . | 4 |