Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6001 | Find the angle between vectors $ \left(-7,~5\right)$ and $\left(6,~1\right)$. | 1 |
| 6002 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~4\right) $ . | 1 |
| 6003 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 1 |
| 6004 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~10\right) $ . | 1 |
| 6005 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 1 |
| 6006 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~4\right) $ . | 1 |
| 6007 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-8,~-7\right) $ and $ \vec{v_2} = \left(9,~7,~-3\right) $ . | 1 |
| 6008 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~0\right) $ . | 1 |
| 6009 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~-8,~-7\right) $ and $ \vec{v_2} = \left(6,~7,~8\right) $ . | 1 |
| 6010 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~7,~8\right) $ and $ \vec{v_2} = \left(-3,~-8,~-7\right) $ . | 1 |
| 6011 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 13 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
| 6012 | Determine whether the vectors $ \vec{v_1} = \left(3,~3434\right) $ and $ \vec{v_2} = \left(343,~434\right) $ are linearly independent or dependent. | 1 |
| 6013 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-3\right) $ . | 1 |
| 6014 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 6015 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 6016 | Find the projection of the vector $ \vec{v_1} = \left(1,~1\right) $ on the vector $ \vec{v_2} = \left(2,~5\right) $. | 1 |
| 6017 | Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
| 6018 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
| 6019 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 8 },~\dfrac{ 7 }{ 8 }\right) $ . | 1 |
| 6020 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 8 },~\dfrac{ 7 }{ 8 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
| 6021 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 8 },~\dfrac{ 7 }{ 8 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
| 6022 | Find the difference of the vectors $ \vec{v_1} = \left(41.4908,~-90.4916\right) $ and $ \vec{v_2} = \left(41.4908,~-90.4914\right) $ . | 1 |
| 6023 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-8\right) $ . | 1 |
| 6024 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-8\right) $ . | 1 |
| 6025 | Find the angle between vectors $ \left(6,~-8\right)$ and $\left(\dfrac{ 49641 }{ 12500 },~\dfrac{ 23923 }{ 50000 }\right)$. | 1 |
| 6026 | Find the angle between vectors $ \left(6,~-8\right)$ and $\left(-\dfrac{ 19641 }{ 12500 },~-\dfrac{ 183923 }{ 50000 }\right)$. | 1 |
| 6027 | Find the angle between vectors $ \left(2,~4,~-3\right)$ and $\left(-4,~4,~6\right)$. | 1 |
| 6028 | Find the angle between vectors $ \left(0,~-1\right)$ and $\left(-2,~3\right)$. | 1 |
| 6029 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(2,~8\right) $ . | 1 |
| 6030 | Find the difference of the vectors $ \vec{v_1} = \left(4200,~180\right) $ and $ \vec{v_2} = \left(7817,~141\right) $ . | 1 |
| 6031 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2\right) $ . | 1 |
| 6032 | Find the angle between vectors $ \left(4,~2\right)$ and $\left(2,~8\right)$. | 1 |
| 6033 | Find the difference of the vectors $ \vec{v_1} = \left(7817,~141\right) $ and $ \vec{v_2} = \left(4200,~180\right) $ . | 1 |
| 6034 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-6,~-2,~8\right) $ and $ \vec{v_2} = \left(-4,~-7,~3\right) $ . | 1 |
| 6035 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-8\right) $ and $ \vec{v_2} = \left(-7,~3\right) $ . | 1 |
| 6036 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 7 }{ 10 },~\dfrac{ 11 }{ 10 },~-\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 1 }{ 7 },~\dfrac{ 9 }{ 7 },~-\dfrac{ 3 }{ 7 }\right) $ . | 1 |
| 6037 | Find the angle between vectors $ \left(-\dfrac{ 7 }{ 10 },~\dfrac{ 11 }{ 10 },~-\dfrac{ 4 }{ 5 }\right)$ and $\left(-\dfrac{ 1 }{ 7 },~\dfrac{ 9 }{ 7 },~-\dfrac{ 3 }{ 7 }\right)$. | 1 |
| 6038 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-10,~0\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
| 6039 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 1 }{ 2 },~0\right) $ . | 1 |
| 6040 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 6041 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 6042 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~2\right) $ and $ \vec{v_2} = \left(7,~9,~2\right) $ . | 1 |
| 6043 | Find the angle between vectors $ \left(3,~2,~2\right)$ and $\left(7,~9,~2\right)$. | 1 |
| 6044 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-1\right) $ . | 1 |
| 6045 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 3 },~-\dfrac{ 1 }{ 3 },~-\dfrac{ 2 }{ 3 }\right) $, $ \vec{v_2} = \left(\dfrac{ 2 }{ 3 },~\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 11 }}{ 6 }\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 6046 | Find the magnitude of the vector $ \| \vec{v} \| = \left(25,~23\right) $ . | 1 |
| 6047 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~3,~3\right) $ and $ \vec{v_2} = \left(3,~-1,~2\right) $ . | 1 |
| 6048 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~9,~2\right) $ and $ \vec{v_2} = \left(-7,~9,~2\right) $ . | 1 |
| 6049 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~2,~2\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 6050 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~10,~-6\right) $ . | 1 |
