Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4451 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~6,~-6\right) $ . | 1 |
| 4452 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~7,~-6\right) $ . | 1 |
| 4453 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(1,~0,~-1\right) $ . | 1 |
| 4454 | Find the angle between vectors $ \left(1,~-2,~3\right)$ and $\left(1,~0,~-1\right)$. | 1 |
| 4455 | Find the angle between vectors $ \left(-7,~-6,~9\right)$ and $\left(5,~-3,~4\right)$. | 1 |
| 4456 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-2\right) $ . | 1 |
| 4457 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5.2,~2.5,~-4.5\right) $ and $ \vec{v_2} = \left(-3,~4,~-1.25\right) $ . | 1 |
| 4458 | Find the projection of the vector $ \vec{v_1} = \left(40,~-30\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 1 |
| 4459 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
| 4460 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~7\right) $ . | 1 |
| 4461 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 4462 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 1255409246 }{ 25 },~\dfrac{ 19953913977 }{ 1000 },~\dfrac{ 3794012556 }{ 125 }\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
| 4463 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~3,~1\right) $ and $ \vec{v_2} = \left(-2,~0,~-1\right) $ . | 1 |
| 4464 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~-2\right) $ and $ \vec{v_2} = \left(-2,~1,~7\right) $ . | 1 |
| 4465 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 24 }{ 5 },~0,~0\right) $ . | 1 |
| 4466 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 353 }{ 40 },~\dfrac{ 1257 }{ 1000 },~-\dfrac{ 3 }{ 200 }\right) $ . | 1 |
| 4467 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(1,~3,~0\right) $ . | 1 |
| 4468 | Find the sum of the vectors $ \vec{v_1} = \left(6,~9,~3\right) $ and $ \vec{v_2} = \left(2,~6,~0\right) $ . | 1 |
| 4469 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(4,~12,~0\right) $ . | 1 |
| 4470 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~1\right) $ . | 1 |
| 4471 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~15,~1\right) $ . | 1 |
| 4472 | Find the sum of the vectors $ \vec{v_1} = \left(14,~6,~10 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(8,~4,~12 \sqrt{ 3 }\right) $ . | 1 |
| 4473 | Find the sum of the vectors $ \vec{v_1} = \left(28,~12,~20 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(2,~1,~3 \sqrt{ 3 }\right) $ . | 1 |
| 4474 | Find the difference of the vectors $ \vec{v_1} = \left(28,~12,~20 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(2,~1,~3 \sqrt{ 3 }\right) $ . | 1 |
| 4475 | Find the sum of the vectors $ \vec{v_1} = \left(7,~3,~5 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(6,~3,~9 \sqrt{ 3 }\right) $ . | 1 |
| 4476 | Find the magnitude of the vector $ \| \vec{v} \| = \left(13,~6,~14 \sqrt{ 3 }\right) $ . | 1 |
| 4477 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 1 |
| 4478 | Find the sum of the vectors $ \vec{v_1} = \left(-9,~5\right) $ and $ \vec{v_2} = \left(9,~-5\right) $ . | 1 |
| 4479 | Determine whether the vectors $ \vec{v_1} = \left(0,~-4,~0\right) $, $ \vec{v_2} = \left(6,~1,~-2\right) $ and $ \vec{v_3} = \left(5,~2,~1\right)$ are linearly independent or dependent. | 1 |
| 4480 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 1 |
| 4481 | Find the angle between vectors $ \left(-11,~0\right)$ and $\left(-5,~0\right)$. | 1 |
| 4482 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~4,~4\right) $ and $ \vec{v_2} = \left(6,~6,~6 \sqrt{ 2 }\right) $ . | 1 |
| 4483 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~4,~4\right) $ . | 1 |
| 4484 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~6,~6 \sqrt{ 2 }\right) $ . | 1 |
| 4485 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2,~6\right) $ and $ \vec{v_2} = \left(6,~3,~2\right) $ . | 1 |
| 4486 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~5,~5\right) $ and $ \vec{v_2} = \left(-4,~-7,~3\right) $ . | 1 |
| 4487 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~4,~5\right) $ and $ \vec{v_2} = \left(-4,~-7,~3\right) $ . | 1 |
| 4488 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~-7\right) $ and $ \vec{v_2} = \left(1,~1,~-1\right) $ . | 1 |
| 4489 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~-1\right) $ and $ \vec{v_2} = \left(3,~4,~-7\right) $ . | 1 |
| 4490 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-4,~3\right) $ and $ \vec{v_2} = \left(1,~-2,~-4\right) $ . | 1 |
| 4491 | Find the magnitude of the vector $ \| \vec{v} \| = \left(22,~7,~2\right) $ . | 1 |
| 4492 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-1,~0\right) $ and $ \vec{v_2} = \left(-1,~1,~1\right) $ . | 1 |
| 4493 | Determine whether the vectors $ \vec{v_1} = \left(-1,~5,~0\right) $, $ \vec{v_2} = \left(-2,~2,~2\right) $ and $ \vec{v_3} = \left(10,~-26,~-6\right)$ are linearly independent or dependent. | 1 |
| 4494 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-2,~-7\right) $ and $ \vec{v_2} = \left(-15,~-9,~-11\right) $ . | 1 |
| 4495 | Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~-5\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ . | 1 |
| 4496 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~3,~3\right) $ . | 1 |
| 4497 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-1\right) $ and $ \vec{v_2} = \left(-1,~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
| 4498 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-1\right) $ and $ \vec{v_2} = \left(-1,~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
| 4499 | Find the sum of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(12,~0\right) $ . | 1 |
| 4500 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~6,~6\right) $ and $ \vec{v_2} = \left(14,~-1,~13\right) $ . | 1 |
