Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5251 | Find the sum of the vectors $ \vec{v_1} = \left(4,~0,~0\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
| 5252 | Find the projection of the vector $ \vec{v_1} = \left(1,~3,~0\right) $ on the vector $ \vec{v_2} = \left(4,~2,~0\right) $. | 1 |
| 5253 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2,~3\right) $ . | 1 |
| 5254 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(0,~2,~4\right) $ . | 1 |
| 5255 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(0,~2,~4\right) $ . | 1 |
| 5256 | Find the angle between vectors $ \left(1,~-2,~3\right)$ and $\left(0,~2,~4\right)$. | 1 |
| 5257 | Find the difference of the vectors $ \vec{v_1} = \left(-8,~3\right) $ and $ \vec{v_2} = \left(2,~8\right) $ . | 1 |
| 5258 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-5\right) $ and $ \vec{v_2} = \left(-3,~7\right) $ . | 1 |
| 5259 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ . | 1 |
| 5260 | Find the difference of the vectors $ \vec{v_1} = \left(2,~11\right) $ and $ \vec{v_2} = \left(-6,~10\right) $ . | 1 |
| 5261 | Find the projection of the vector $ \vec{v_1} = \left(407,~-4,~288\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $. | 1 |
| 5262 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(5,~45\right) $ . | 1 |
| 5263 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(-2,~-1,~1\right) $ . | 1 |
| 5264 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(-2,~2,~2\right) $ . | 1 |
| 5265 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~8\right) $ . | 1 |
| 5266 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
| 5267 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(2,~2,~0\right) $ . | 1 |
| 5268 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right)$ and $\left(-\dfrac{ 1 }{ 2 },~-\dfrac{ 1 }{ 2 }\right)$. | 1 |
| 5269 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right)$ and $\left(-\dfrac{ 1 }{ 4 },~-\dfrac{ 1 }{ 4 }\right)$. | 1 |
| 5270 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right)$ and $\left(-\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right)$. | 1 |
| 5271 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-2\right) $ and $ \vec{v_2} = \left(11,~-6\right) $ . | 1 |
| 5272 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-2\right) $ . | 1 |
| 5273 | Find the angle between vectors $ \left(\sqrt{ 3 },~-3\right)$ and $\left(-1,~-1\right)$. | 1 |
| 5274 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-6,~9\right) $ . | 1 |
| 5275 | Determine whether the vectors $ \vec{v_1} = \left(4,~-5\right) $ and $ \vec{v_2} = \left(12,~-15\right) $ are linearly independent or dependent. | 1 |
| 5276 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~90\right) $ . | 1 |
| 5277 | Find the projection of the vector $ \vec{v_1} = \left(7,~-3\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 1 |
| 5278 | Find the sum of the vectors $ \vec{v_1} = \left(9,~4\right) $ and $ \vec{v_2} = \left(4,~0\right) $ . | 1 |
| 5279 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 1 |
| 5280 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~4\right) $ . | 1 |
| 5281 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4 \sqrt{ 3 },~-2\right) $ . | 1 |
| 5282 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~0\right) $ . | 1 |
| 5283 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~8\right) $ . | 1 |
| 5284 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-2\right) $ and $ \vec{v_2} = \left(-6,~4\right) $ . | 1 |
| 5285 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(3,~6\right) $ . | 1 |
| 5286 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-5\right) $ . | 1 |
| 5287 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-3,~1\right) $ . | 1 |
| 5288 | Find the difference of the vectors $ \vec{v_1} = \left(2,~7\right) $ and $ \vec{v_2} = \left(8,~0\right) $ . | 1 |
| 5289 | Find the difference of the vectors $ \vec{v_1} = \left(4,~14\right) $ and $ \vec{v_2} = \left(-24,~0\right) $ . | 1 |
| 5290 | Find the sum of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 1 |
| 5291 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-5\right) $ . | 1 |
| 5292 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~-2\right) $ . | 1 |
| 5293 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~4\right) $ . | 1 |
| 5294 | Find the magnitude of the vector $ \| \vec{v} \| = \left(17,~-11,~55\right) $ . | 1 |
| 5295 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-5\right) $ . | 1 |
| 5296 | Find the angle between vectors $ \left(\sqrt{ 3 },~-1\right)$ and $\left(0,~5\right)$. | 1 |
| 5297 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 1 |
| 5298 | Find the angle between vectors $ \left(1,~-2\right)$ and $\left(1,~4\right)$. | 1 |
| 5299 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-8\right) $ . | 1 |
| 5300 | Calculate the cross product of the vectors $ \vec{v_1} = \left(10,~0,~-8\right) $ and $ \vec{v_2} = \left(3,~-1,~-12\right) $ . | 1 |
