Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4901 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~20,~12\right) $ and $ \vec{v_2} = \left(5,~-5,~-4\right) $ . | 1 |
| 4902 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~20,~12\right) $ and $ \vec{v_2} = \left(5,~-5,~-4\right) $ . | 1 |
| 4903 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 43 }{ 5 },~1,~7\right) $ and $ \vec{v_2} = \left(\dfrac{ 49 }{ 5 },~\dfrac{ 19 }{ 2 },~\dfrac{ 29 }{ 10 }\right) $ . | 1 |
| 4904 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 7 },~\dfrac{ 3 }{ 7 }\right) $ . | 1 |
| 4905 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ . | 1 |
| 4906 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ . | 1 |
| 4907 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ . | 1 |
| 4908 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ . | 1 |
| 4909 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(3,~8\right)$. | 1 |
| 4910 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~7,~3\right) $ and $ \vec{v_2} = \left(4,~4,~1\right) $ . | 1 |
| 4911 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-5,~1\right) $ and $ \vec{v_2} = \left(-4,~1,~5\right) $ . | 1 |
| 4912 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 8 }{ 3 },~0,~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 1 }{ 3 },~-3\right) $ . | 1 |
| 4913 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~-1\right) $ and $ \vec{v_2} = \left(0,~-1,~7\right) $ . | 1 |
| 4914 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~1\right) $ and $ \vec{v_2} = \left(3,~0,~-2\right) $ . | 1 |
| 4915 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~6,~0\right) $ and $ \vec{v_2} = \left(1,~0,~-6\right) $ . | 1 |
| 4916 | Find the projection of the vector $ \vec{v_1} = \left(-1,~2\right) $ on the vector $ \vec{v_2} = \left(7,~17\right) $. | 1 |
| 4917 | Find the angle between vectors $ \left(-1,~2\right)$ and $\left(7,~17\right)$. | 1 |
| 4918 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~7\right) $ and $ \vec{v_2} = \left(1,~22\right) $ . | 1 |
| 4919 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~9,~0\right) $ and $ \vec{v_2} = \left(8,~0,~-1\right) $ . | 1 |
| 4920 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~7\right) $ . | 1 |
| 4921 | Find the angle between vectors $ \left(-7,~7\right)$ and $\left(1,~22\right)$. | 1 |
| 4922 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~0,~-1\right) $ . | 1 |
| 4923 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4,~5\right) $ . | 1 |
| 4924 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4,~3\right) $ . | 1 |
| 4925 | Determine whether the vectors $ \vec{v_1} = \left(1,~-4\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ are linearly independent or dependent. | 1 |
| 4926 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-4\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ . | 1 |
| 4927 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~3\right) $ and $ \vec{v_2} = \left(1,~-3,~2\right) $ . | 1 |
| 4928 | Find the magnitude of the vector $ \| \vec{v} \| = \left(17,~-3,~-13\right) $ . | 1 |
| 4929 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-5,~7\right) $ . | 1 |
| 4930 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~1\right) $ . | 1 |
| 4931 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~3,~-2\right) $ . | 1 |
| 4932 | Find the difference of the vectors $ \vec{v_1} = \left(6,~-2,~2\right) $ and $ \vec{v_2} = \left(3,~3,~-2\right) $ . | 1 |
| 4933 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~-5,~4\right) $ . | 1 |
| 4934 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~1\right) $ on the vector $ \vec{v_2} = \left(3,~3,~-2\right) $. | 1 |
| 4935 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~1\right) $ . | 1 |
| 4936 | Find the projection of the vector $ \vec{v_1} = \left(3,~3,~-2\right) $ on the vector $ \vec{v_2} = \left(2,~2,~-4\right) $. | 1 |
| 4937 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(-5,~5,~0\right) $ . | 1 |
| 4938 | Find the difference of the vectors $ \vec{v_1} = \left(1,~0,~8\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
| 4939 | Find the difference of the vectors $ \vec{v_1} = \left(0,~1,~3\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
| 4940 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~7\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 4941 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(-5,~5,~0\right) $ . | 1 |
| 4942 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(-5,~5,~0\right) $ . | 1 |
| 4943 | Find the angle between vectors $ \left(3,~-5\right)$ and $\left(4,~3\right)$. | 1 |
| 4944 | Find the angle between vectors $ \left(1,~1,~5\right)$ and $\left(5,~-5,~2\right)$. | 1 |
| 4945 | Find the sum of the vectors $ \vec{v_1} = \left(1,~11\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ . | 1 |
| 4946 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~5\right) $ on the vector $ \vec{v_2} = \left(5,~-5,~2\right) $. | 1 |
| 4947 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~-3\right) $ and $ \vec{v_2} = \left(1,~-1,~3\right) $ . | 1 |
| 4948 | Calculate the dot product of the vectors $ \vec{v_1} = \left(18,~-15,~-1\right) $ and $ \vec{v_2} = \left(1,~1,~3\right) $ . | 1 |
| 4949 | Find the difference of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 1 |
| 4950 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1729 }{ 10000 },~\dfrac{ 24739 }{ 10000 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 5591 }{ 2500 },~-\dfrac{ 5023 }{ 5000 }\right) $ . | 1 |
