Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 351 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-2,~7\right) $ and $ \vec{v_2} = \left(4,~3,~-2\right) $ . | 3 |
| 352 | Find the sum of the vectors $ \vec{v_1} = \left(12,~9\right) $ and $ \vec{v_2} = \left(-6,~\dfrac{ 1039 }{ 100 }\right) $ . | 3 |
| 353 | Find the projection of the vector $ \vec{v_1} = \left(1,~1\right) $ on the vector $ \vec{v_2} = \left(6,~3\right) $. | 3 |
| 354 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 3 |
| 355 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(-2,~-5\right) $ . | 3 |
| 356 | Find the angle between vectors $ \left(-3,~-5\right)$ and $\left(-4,~-2\right)$. | 3 |
| 357 | Find the difference of the vectors $ \vec{v_1} = \left(-7,~0\right) $ and $ \vec{v_2} = \left(8,~-1\right) $ . | 3 |
| 358 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(9,~9\right) $ . | 3 |
| 359 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 231 }{ 10 },~-\dfrac{ 16 }{ 5 }\right) $ . | 3 |
| 360 | Find the projection of the vector $ \vec{v_1} = \left(0,~-5,~7\right) $ on the vector $ \vec{v_2} = \left(-5,~1,~5\right) $. | 3 |
| 361 | Find the projection of the vector $ \vec{v_1} = \left(3020,~2800\right) $ on the vector $ \vec{v_2} = \left(1,~-1\right) $. | 3 |
| 362 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-1,~2\right) $ . | 3 |
| 363 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 21 }{ 10 },~-\dfrac{ 16 }{ 5 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 3 |
| 364 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 39 }{ 10 },~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 3 |
| 365 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~1,~2\right) $ . | 3 |
| 366 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 3 |
| 367 | Determine whether the vectors $ \vec{v_1} = \left(4,~5,~7\right) $, $ \vec{v_2} = \left(6,~7,~6\right) $ and $ \vec{v_3} = \left(-4,~-7,~3\right)$ are linearly independent or dependent. | 3 |
| 368 | Determine whether the vectors $ \vec{v_1} = \left(2,~-8,~8\right) $, $ \vec{v_2} = \left(16,~-72,~71\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 3 |
| 369 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~2\right) $ . | 3 |
| 370 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-3\right) $ . | 3 |
| 371 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 3 |
| 372 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2\right) $ . | 3 |
| 373 | Find the sum of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 3 |
| 374 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 3 |
| 375 | Find the angle between vectors $ \left(2,~2,~2\right)$ and $\left(1,~-1,~1\right)$. | 3 |
| 376 | Find the projection of the vector $ \vec{v_1} = \left(3,~6\right) $ on the vector $ \vec{v_2} = \left(-2,~9\right) $. | 3 |
| 377 | Find the sum of the vectors $ \vec{v_1} = \left(37.8,~39.6\right) $ and $ \vec{v_2} = \left(4.73,~-4.99\right) $ . | 3 |
| 378 | Find the sum of the vectors $ \vec{v_1} = \left(-19.05,~11\right) $ and $ \vec{v_2} = \left(-5.73,~-32.5\right) $ . | 3 |
| 379 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-12\right) $ and $ \vec{v_2} = \left(-12,~-15\right) $ . | 3 |
| 380 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~\sqrt{ 12 }\right) $ . | 3 |
| 381 | Find the difference of the vectors $ \vec{v_1} = \left(8,~2\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ . | 3 |
| 382 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(2,~10\right) $ . | 3 |
| 383 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~5\right) $ . | 3 |
| 384 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 3 |
| 385 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 3 |
| 386 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~1\right) $ . | 3 |
| 387 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(5,~0.5\right) $ . | 3 |
| 388 | Find the sum of the vectors $ \vec{v_1} = \left(-36,~4\right) $ and $ \vec{v_2} = \left(21,~13\right) $ . | 3 |
| 389 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 3 |
| 390 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(9,~8\right) $ . | 3 |
| 391 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 3 |
| 392 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-4\right) $ . | 3 |
| 393 | Find the difference of the vectors $ \vec{v_1} = \left(10,~3\right) $ and $ \vec{v_2} = \left(4,~8\right) $ . | 3 |
| 394 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 3 |
| 395 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-6\right) $ . | 3 |
| 396 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~-1\right) $ . | 3 |
| 397 | Find the difference of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(8,~-12\right) $ . | 3 |
| 398 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 3 |
| 399 | Find the difference of the vectors $ \vec{v_1} = \left(-24,~21\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 3 |
| 400 | Find the projection of the vector $ \vec{v_1} = \left(6,~7\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 3 |
