Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4951 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 24093 }{ 10000 },~\dfrac{ 14693 }{ 10000 }\right) $ . | 1 |
| 4952 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 24093 }{ 10000 },~\dfrac{ 14693 }{ 10000 }\right) $ and $ \vec{v_2} = \left(0,~-150\right) $ . | 1 |
| 4953 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(-2,~1,~1\right) $ . | 1 |
| 4954 | Find the angle between vectors $ \left(-4,~-1,~0\right)$ and $\left(1,~3,~-2\right)$. | 1 |
| 4955 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~3,~-2\right) $ . | 1 |
| 4956 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~3,~-2\right) $ . | 1 |
| 4957 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~0,~-1\right) $ and $ \vec{v_2} = \left(0,~-1,~3\right) $ . | 1 |
| 4958 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~1,~5\right) $ and $ \vec{v_2} = \left(2,~-1,~4\right) $ . | 1 |
| 4959 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-2,~2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 4960 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
| 4961 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ . | 1 |
| 4962 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
| 4963 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~6\right) $ . | 1 |
| 4964 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 1 |
| 4965 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~\sqrt{ 12 }\right) $ . | 1 |
| 4966 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-12,~20\right) $ . | 1 |
| 4967 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~12,~3\right) $ and $ \vec{v_2} = \left(15,~2,~-7\right) $ . | 1 |
| 4968 | Find the sum of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(8,~3\right) $ . | 1 |
| 4969 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(8,~3\right) $ . | 1 |
| 4970 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~7\right) $ and $ \vec{v_2} = \left(-6,~3\right) $ . | 1 |
| 4971 | Find the angle between vectors $ \left(1,~0\right)$ and $\left(2,~0\right)$. | 1 |
| 4972 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 4973 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~-4\right) $ . | 1 |
| 4974 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~-4\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 1 |
| 4975 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(7,~3\right) $ . | 1 |
| 4976 | Find the magnitude of the vector $ \| \vec{v} \| = \left(13,~48\right) $ . | 1 |
| 4977 | Find the difference of the vectors $ \vec{v_1} = \left(13,~48\right) $ and $ \vec{v_2} = \left(6,~120\right) $ . | 1 |
| 4978 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
| 4979 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(7,~1\right) $ . | 1 |
| 4980 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(7,~1\right) $ . | 1 |
| 4981 | Find the sum of the vectors $ \vec{v_1} = \left(2,~8\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 1 |
| 4982 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~4\right) $ and $ \vec{v_2} = \left(2,~-6\right) $ . | 1 |
| 4983 | Find the angle between vectors $ \left(-1,~-1\right)$ and $\left(-1,~1\right)$. | 1 |
| 4984 | Find the angle between vectors $ \left(7,~4\right)$ and $\left(4,~-7\right)$. | 1 |
| 4985 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~4\right) $ and $ \vec{v_2} = \left(4,~-7\right) $ . | 1 |
| 4986 | Find the angle between vectors $ \left(1,~1\right)$ and $\left(\dfrac{ 34641 }{ 20000 },~3\right)$. | 1 |
| 4987 | Find the angle between vectors $ \left(1,~1\right)$ and $\left(\sqrt{ 3 },~3\right)$. | 1 |
| 4988 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(-15,~-20\right)$. | 1 |
| 4989 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4\right) $ . | 1 |
| 4990 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-9\right) $ and $ \vec{v_2} = \left(-1,~6\right) $ . | 1 |
| 4991 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(5,~7\right) $ . | 1 |
| 4992 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~7\right) $ and $ \vec{v_2} = \left(-5,~4\right) $ . | 1 |
| 4993 | Find the angle between vectors $ \left(3,~1\right)$ and $\left(3,~-2\right)$. | 1 |
| 4994 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(1,~-4\right) $ . | 1 |
| 4995 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 519 }{ 1000 },~\dfrac{ 3 }{ 1000 },~\dfrac{ 1 }{ 1000 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 125 },~\dfrac{ 63 }{ 250 },~-\dfrac{ 73 }{ 500 }\right) $ . | 1 |
| 4996 | Find the angle between vectors $ \left(\dfrac{ 519 }{ 1000 },~\dfrac{ 3 }{ 1000 },~\dfrac{ 1 }{ 1000 }\right)$ and $\left(\dfrac{ 1 }{ 125 },~\dfrac{ 63 }{ 250 },~-\dfrac{ 73 }{ 500 }\right)$. | 1 |
| 4997 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~1\right) $ . | 1 |
| 4998 | Find the angle between vectors $ \left(-18.3,~21.353\right)$ and $\left(60.743,~47.76\right)$. | 1 |
| 4999 | Find the angle between vectors $ \left(0,~-1\right)$ and $\left(-6,~0\right)$. | 1 |
| 5000 | Find the angle between vectors $ \left(5,~0\right)$ and $\left(-1,~-1\right)$. | 1 |
