Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 301 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3 \sqrt{ 3 },~-3\right) $ . | 3 |
| 302 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-3,~0\right) $ . | 3 |
| 303 | Find the angle between vectors $ \left(\dfrac{ 69503 }{ 100000 },~0.0652,~\dfrac{ 30519 }{ 3125 }\right)$ and $\left(0,~0,~\dfrac{ 49 }{ 5 }\right)$. | 3 |
| 304 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 69503 }{ 100000 },~0.0652,~\dfrac{ 30519 }{ 3125 }\right) $ and $ \vec{v_2} = \left(0,~0,~\dfrac{ 49 }{ 5 }\right) $ . | 3 |
| 305 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~2\right) $ and $ \vec{v_2} = \left(1,~1,~4\right) $ . | 3 |
| 306 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~1\right) $ and $ \vec{v_2} = \left(4,~3,~-1\right) $ . | 3 |
| 307 | Find the angle between vectors $ \left(2,~10\right)$ and $\left(5,~-2\right)$. | 3 |
| 308 | Find the angle between vectors $ \left(7,~-1\right)$ and $\left(2,~2\right)$. | 3 |
| 309 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ . | 3 |
| 310 | Find the difference of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 3 |
| 311 | Find the projection of the vector $ \vec{v_1} = \left(-1,~1\right) $ on the vector $ \vec{v_2} = \left(3,~3\right) $. | 3 |
| 312 | Find the angle between vectors $ \left(1,~-4\right)$ and $\left(2,~0\right)$. | 3 |
| 313 | Find the angle between vectors $ \left(-1,~0\right)$ and $\left(0,~5\right)$. | 3 |
| 314 | Find the angle between vectors $ \left(-2,~4\right)$ and $\left(8,~-16\right)$. | 3 |
| 315 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 3 |
| 316 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~1\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ . | 3 |
| 317 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~7\right) $ . | 3 |
| 318 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-36,~-37\right) $ . | 3 |
| 319 | Find the sum of the vectors $ \vec{v_1} = \left(-28,~4\right) $ and $ \vec{v_2} = \left(11,~15\right) $ . | 3 |
| 320 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(-3,~8\right) $ . | 3 |
| 321 | Find the angle between vectors $ \left(5,~-2\right)$ and $\left(-4,~3\right)$. | 3 |
| 322 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~5\right) $ . | 3 |
| 323 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~1\right) $ and $ \vec{v_2} = \left(1,~8\right) $ . | 3 |
| 324 | Find the projection of the vector $ \vec{v_1} = \left(-4,~6\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 3 |
| 325 | Find the angle between vectors $ \left(-2,~5,~-3\right)$ and $\left(4,~-6,~8\right)$. | 3 |
| 326 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-1,~2\right) $ and $ \vec{v_2} = \left(4,~3,~-2\right) $ . | 3 |
| 327 | Find the angle between vectors $ \left(1,~-3\right)$ and $\left(5,~\dfrac{ 1 }{ 2 }\right)$. | 3 |
| 328 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-2\right) $ . | 3 |
| 329 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3\right) $ . | 3 |
| 330 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(0,~2\right) $ . | 3 |
| 331 | Find the difference of the vectors $ \vec{v_1} = \left(0,~10\right) $ and $ \vec{v_2} = \left(0,~10\right) $ . | 3 |
| 332 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-2\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 3 |
| 333 | Determine whether the vectors $ \vec{v_1} = \left(3,~-2,~4\right) $, $ \vec{v_2} = \left(1,~-2,~3\right) $ and $ \vec{v_3} = \left(3,~2,~-1\right)$ are linearly independent or dependent. | 3 |
| 334 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-\sqrt{ 3 },~\dfrac{ 3 }{ 2 }\right) $ . | 3 |
| 335 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 3 |
| 336 | Find the angle between vectors $ \left(9,~2\right)$ and $\left(-8,~-12\right)$. | 3 |
| 337 | Find the angle between vectors $ \left(9,~2\right)$ and $\left(12,~-8\right)$. | 3 |
| 338 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 3 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ . | 3 |
| 339 | Find the difference of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(\dfrac{ 22 }{ 5 },~\dfrac{ 11 }{ 5 }\right) $ . | 3 |
| 340 | Find the angle between vectors $ \left(4,~2\right)$ and $\left(4.4721,~2.2361\right)$. | 3 |
| 341 | Determine whether the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(-10,~7\right) $ are linearly independent or dependent. | 3 |
| 342 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(-10,~7\right) $ . | 3 |
| 343 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~3\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 2 },~0,~3\right) $ . | 3 |
| 344 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~11\right) $ and $ \vec{v_2} = \left(10,~4\right) $ . | 3 |
| 345 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~3\right) $ . | 3 |
| 346 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-4\right) $ . | 3 |
| 347 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(-3,~-3\right) $ . | 3 |
| 348 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 2 },~-\dfrac{ 3 }{ 2 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~-\dfrac{ 1 }{ 2 },~2\right) $ . | 3 |
| 349 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(-7,~6\right) $ . | 3 |
| 350 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2\right) $ . | 3 |
