Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 401 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~12\right) $ . | 3 |
| 402 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 4 },~\dfrac{ 2 }{ 5 }\right) $ and $ \vec{v_2} = \left(-5,~-\dfrac{ 5 }{ 4 }\right) $ . | 3 |
| 403 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 3 |
| 404 | Find the angle between vectors $ \left(7,~5\right)$ and $\left(0,~8\right)$. | 3 |
| 405 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 3 |
| 406 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(0,~6\right) $ . | 3 |
| 407 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(0,~-6\right) $ . | 3 |
| 408 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-1\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 3 |
| 409 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0\right) $ . | 3 |
| 410 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~3\right) $ . | 3 |
| 411 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~0\right) $ . | 3 |
| 412 | Find the angle between vectors $ \left(4,~1\right)$ and $\left(1,~4\right)$. | 3 |
| 413 | Find the difference of the vectors $ \vec{v_1} = \left(-24,~21\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 3 |
| 414 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 3 |
| 415 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~8\right) $ . | 3 |
| 416 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~1\right) $ and $ \vec{v_2} = \left(11,~15\right) $ . | 3 |
| 417 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 3 |
| 418 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 3 |
| 419 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~4\right) $ . | 3 |
| 420 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 42 }{ 5 },~0\right) $ . | 3 |
| 421 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(3,~24\right) $ . | 3 |
| 422 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~60\right) $ . | 3 |
| 423 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 5 }{ 13 },~\dfrac{ 12 }{ 13 }\right) $ . | 3 |
| 424 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-2,~-2\right) $ . | 3 |
| 425 | Find the projection of the vector $ \vec{v_1} = \left(6,~7\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 3 |
| 426 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~-1\right) $ . | 3 |
| 427 | Find the angle between vectors $ \left(-4,~6\right)$ and $\left(2,~-1\right)$. | 2 |
| 428 | Find the sum of the vectors $ \vec{v_1} = \left(5,~16\right) $ and $ \vec{v_2} = \left(8,~4\right) $ . | 2 |
| 429 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 2 |
| 430 | Find the projection of the vector $ \vec{v_1} = \left(0,~4\right) $ on the vector $ \vec{v_2} = \left(-1,~-3\right) $. | 2 |
| 431 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-1\right) $ . | 2 |
| 432 | Find the angle between vectors $ \left(-2,~-5\right)$ and $\left(-5,~0\right)$. | 2 |
| 433 | Find the angle between vectors $ \left(-2,~-5\right)$ and $\left(-5,~4\right)$. | 2 |
| 434 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~5\right) $ . | 2 |
| 435 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~-5\right) $ . | 2 |
| 436 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~-4\right) $ and $ \vec{v_2} = \left(-6,~-2\right) $ . | 2 |
| 437 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 2 |
| 438 | Find the projection of the vector $ \vec{v_1} = \left(-3,~5,~2\right) $ on the vector $ \vec{v_2} = \left(0,~1,~0\right) $. | 2 |
| 439 | Find the projection of the vector $ \vec{v_1} = \left(4,~3\right) $ on the vector $ \vec{v_2} = \left(0,~1\right) $. | 2 |
| 440 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-3\right) $ . | 2 |
| 441 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-5\right) $ . | 2 |
| 442 | Find the angle between vectors $ \left(-4,~1\right)$ and $\left(-5,~2\right)$. | 2 |
| 443 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(15,~9\right) $ . | 2 |
| 444 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-9\right) $ . | 2 |
| 445 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~4\right) $ . | 2 |
| 446 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~1\right) $ . | 2 |
| 447 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-3,~1\right) $ and $ \vec{v_2} = \left(4,~9,~2\right) $ . | 2 |
| 448 | Find the difference of the vectors $ \vec{v_1} = \left(2,~7\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 2 |
| 449 | Find the projection of the vector $ \vec{v_1} = \left(2,~-5\right) $ on the vector $ \vec{v_2} = \left(5,~1\right) $. | 2 |
| 450 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~6,~2\right) $ and $ \vec{v_2} = \left(2,~3,~0\right) $ . | 2 |
