Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4001 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1\right) $ . | 1 |
| 4002 | Find the angle between vectors $ \left(3,~1\right)$ and $\left(-1,~4\right)$. | 1 |
| 4003 | Find the difference of the vectors $ \vec{v_1} = \left(180,~32\right) $ and $ \vec{v_2} = \left(210,~38\right) $ . | 1 |
| 4004 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 152649 }{ 1000 },~\dfrac{ 190771 }{ 2000 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 82741 }{ 500 },~\dfrac{ 129289 }{ 1000 }\right) $ . | 1 |
| 4005 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-6\right) $ . | 1 |
| 4006 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~6\right) $ . | 1 |
| 4007 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~-3\right) $ and $ \vec{v_2} = \left(-4,~2,~3\right) $ . | 1 |
| 4008 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 371 }{ 50 },~0\right) $ . | 1 |
| 4009 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 1 |
| 4010 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~1,~2\right) $ and $ \vec{v_2} = \left(1,~2,~0\right) $ . | 1 |
| 4011 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1,~-2\right) $ and $ \vec{v_2} = \left(5,~0,~-5\right) $ . | 1 |
| 4012 | Find the difference of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 1 |
| 4013 | Find the difference of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 1 |
| 4014 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~5,~-7\right) $ and $ \vec{v_2} = \left(-1,~3,~-2\right) $ . | 1 |
| 4015 | Find the sum of the vectors $ \vec{v_1} = \left(1,~3,~-10\right) $ and $ \vec{v_2} = \left(7,~-2,~6\right) $ . | 1 |
| 4016 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-9\right) $ and $ \vec{v_2} = \left(8,~-9\right) $ . | 1 |
| 4017 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~-3\right) $ and $ \vec{v_2} = \left(6,~0,~0\right) $ . | 1 |
| 4018 | Find the difference of the vectors $ \vec{v_1} = \left(1,~3,~5\right) $ and $ \vec{v_2} = \left(-\dfrac{ 10 }{ 9 },~-\dfrac{ 5 }{ 9 },~\dfrac{ 10 }{ 9 }\right) $ . | 1 |
| 4019 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 19 }{ 9 },~\dfrac{ 32 }{ 9 },~\dfrac{ 35 }{ 9 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 10 }{ 9 },~-\dfrac{ 5 }{ 9 },~\dfrac{ 10 }{ 9 }\right) $ . | 1 |
| 4020 | Find the magnitude of the vector $ \| \vec{v} \| = \left(144,~0,~0\right) $ . | 1 |
| 4021 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2\right) $ . | 1 |
| 4022 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-2 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(6,~-2 \sqrt{ 3 }\right) $ . | 1 |
| 4023 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 219 }{ 10 },~1,~-\dfrac{ 15 }{ 2 }\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $. | 1 |
| 4024 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(0,~-4\right) $ . | 1 |
| 4025 | Find the angle between vectors $ \left(-3,~0,~4\right)$ and $\left(0,~1,~-2\right)$. | 1 |
| 4026 | Find the angle between vectors $ \left(2,~5,~4\right)$ and $\left(6,~0,~-3\right)$. | 1 |
| 4027 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 1 |
| 4028 | Find the difference of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 1 |
| 4029 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
| 4030 | Determine whether the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(0,~0\right) $ are linearly independent or dependent. | 1 |
| 4031 | Find the projection of the vector $ \vec{v_1} = \left(2,~-1,~3\right) $ on the vector $ \vec{v_2} = \left(-4,~2,~1\right) $. | 1 |
| 4032 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(-4,~2,~1\right) $ . | 1 |
| 4033 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~9\right) $ . | 1 |
| 4034 | Find the angle between vectors $ \left(3,~4,~5\right)$ and $\left(3,~4,~-5\right)$. | 1 |
| 4035 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4,~-5\right) $ and $ \vec{v_2} = \left(-4,~8,~10\right) $ . | 1 |
| 4036 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4,~-5\right) $ and $ \vec{v_2} = \left(-45,~-5,~-14\right) $ . | 1 |
| 4037 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4,~-5\right) $ and $ \vec{v_2} = \left(-15,~15,~-18\right) $ . | 1 |
| 4038 | Find the angle between vectors $ \left(4,~-2,~5\right)$ and $\left(1,~3,~2\right)$. | 1 |
| 4039 | Find the angle between vectors $ \left(1,~-1,~0\right)$ and $\left(0,~-1,~1\right)$. | 1 |
| 4040 | Find the angle between vectors $ \left(4,~-2,~5\right)$ and $\left(5,~4,~-2\right)$. | 1 |
| 4041 | Find the angle between vectors $ \left(4,~-2,~5\right)$ and $\left(10,~0,~8\right)$. | 1 |
| 4042 | Find the angle between vectors $ \left(4,~-2,~5\right)$ and $\left(5,~-4,~-2\right)$. | 1 |
| 4043 | Find the projection of the vector $ \vec{v_1} = \left(4,~-2,~5\right) $ on the vector $ \vec{v_2} = \left(5,~-4,~-2\right) $. | 1 |
| 4044 | Find the angle between vectors $ \left(4,~-2,~5\right)$ and $\left(-10,~0,~8\right)$. | 1 |
| 4045 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~5,~2\right) $ and $ \vec{v_2} = \left(2,~4,~-2\right) $ . | 1 |
| 4046 | Find the projection of the vector $ \vec{v_1} = \left(-1,~1,~2\right) $ on the vector $ \vec{v_2} = \left(-2,~10,~10\right) $. | 1 |
| 4047 | Find the projection of the vector $ \vec{v_1} = \left(-2,~10,~20\right) $ on the vector $ \vec{v_2} = \left(-1,~1,~2\right) $. | 1 |
| 4048 | Find the projection of the vector $ \vec{v_1} = \left(-2,~10,~10\right) $ on the vector $ \vec{v_2} = \left(-1,~1,~2\right) $. | 1 |
| 4049 | Find the projection of the vector $ \vec{v_1} = \left(-4,~3\right) $ on the vector $ \vec{v_2} = \left(1,~2\right) $. | 1 |
| 4050 | Find the angle between vectors $ \left(\sqrt{ 3 },~-1\right)$ and $\left(0,~7\right)$. | 1 |
