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) $ . | 734 |
| 2 | 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) $ . | 373 |
| 3 | Find the angle between vectors $ \left(2,~1,~-4\right)$ and $\left(3,~-5,~2\right)$. | 182 |
| 4 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ . | 167 |
| 5 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 58 |
| 6 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 41 |
| 7 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 34 |
| 8 | Find the difference of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 28 |
| 9 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 20 |
| 10 | Find the projection of the vector $ \vec{v_1} = \left(3,~2\right) $ on the vector $ \vec{v_2} = \left(5,~-5\right) $. | 17 |
| 11 | Find the projection of the vector $ \vec{v_1} = \left(0,~0\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 14 |
| 12 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4\right) $ . | 13 |
| 13 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-25,~-10\right) $ . | 12 |
| 14 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 5 }{ 3 },~-\dfrac{ 3 }{ 2 }\right) $ . | 11 |
| 15 | | 10 |
| 16 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 10 |
| 17 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 9 |
| 18 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 9 |
| 19 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-4\right) $ . | 9 |
| 20 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-4\right) $ . | 8 |
| 21 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~54\right) $ . | 8 |
| 22 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 8 |
| 23 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 8 |
| 24 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 8 |
| 25 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~6\right) $ and $ \vec{v_2} = \left(-8,~7\right) $ . | 8 |
| 26 | 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 |
| 27 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 39 }{ 10 },~\dfrac{ 23 }{ 20 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 7 |
| 28 | Find the sum of the vectors $ \vec{v_1} = \left(6,~4\right) $ and $ \vec{v_2} = \left(7,~-2\right) $ . | 7 |
| 29 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 7 |
| 30 | 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 |
| 31 | 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 |
| 32 | Determine whether the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ are linearly independent or dependent. | 6 |
| 33 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~8\right) $ . | 6 |
| 34 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~0\right) $ . | 6 |
| 35 | Find the difference of the vectors $ \vec{v_1} = \left(9,~6\right) $ and $ \vec{v_2} = \left(\dfrac{ 609 }{ 65 },~\dfrac{ 348 }{ 65 }\right) $ . | 6 |
| 36 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~5,~8\right) $ . | 6 |
| 37 | Find the projection of the vector $ \vec{v_1} = \left(-4,~3\right) $ on the vector $ \vec{v_2} = \left(5,~12\right) $. | 6 |
| 38 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2\right) $ . | 6 |
| 39 | Find the projection of the vector $ \vec{v_1} = \left(1,~-3\right) $ on the vector $ \vec{v_2} = \left(5,~\dfrac{ 1 }{ 2 }\right) $. | 6 |
| 40 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 6 |
| 41 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 6 |
| 42 | Find the sum of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 6 |
| 43 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~5\right) $ . | 6 |
| 44 | Find the difference of the vectors $ \vec{v_1} = \left(4,~6\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 6 |
| 45 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 4 },~2\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 5 |
| 46 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~4\right) $ . | 5 |
| 47 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 5 |
| 48 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~9\right) $ . | 5 |
| 49 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~4\right) $ . | 5 |
| 50 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 5 |
