Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4401 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-8,~6\right) $ and $ \vec{v_2} = \left(-5,~4,~9\right) $ . | 1 |
| 4402 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-8,~6\right) $ . | 1 |
| 4403 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-8,~6\right) $ and $ \vec{v_2} = \left(-5,~4,~9\right) $ . | 1 |
| 4404 | Find the angle between vectors $ \left(3,~-8,~6\right)$ and $\left(-5,~4,~9\right)$. | 1 |
| 4405 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~3,~4\right) $ and $ \vec{v_2} = \left(5,~3,~-6\right) $ . | 1 |
| 4406 | Find the angle between vectors $ \left(-2,~1,~4\right)$ and $\left(1,~1,~0\right)$. | 1 |
| 4407 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 4408 | Find the angle between vectors $ \left(8,~5\right)$ and $\left(4,~0\right)$. | 1 |
| 4409 | Find the angle between vectors $ \left(3,~2,~-5\right)$ and $\left(12,~8,~-20\right)$. | 1 |
| 4410 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1\right) $ . | 1 |
| 4411 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-4,~1\right) $ . | 1 |
| 4412 | Find the projection of the vector $ \vec{v_1} = \left(15,~10\right) $ on the vector $ \vec{v_2} = \left(-25,~2\right) $. | 1 |
| 4413 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~2\right) $ . | 1 |
| 4414 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~2\right) $ and $ \vec{v_2} = \left(2,~-1,~-3\right) $ . | 1 |
| 4415 | Find the angle between vectors $ \left(8,~1,~-9\right)$ and $\left(8,~1,~9\right)$. | 1 |
| 4416 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 789 }{ 10000 },~\dfrac{ 867 }{ 10000 },~\dfrac{ 1941 }{ 5000 }\right) $ . | 1 |
| 4417 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1,~-4\right) $ and $ \vec{v_2} = \left(2,~8,~1\right) $ . | 1 |
| 4418 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~8,~1\right) $ and $ \vec{v_2} = \left(2,~1,~-4\right) $ . | 1 |
| 4419 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~6,~4\right) $ and $ \vec{v_2} = \left(0,~2,~-3\right) $ . | 1 |
| 4420 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~6,~4\right) $ and $ \vec{v_2} = \left(-26,~6,~4\right) $ . | 1 |
| 4421 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~5\right) $ and $ \vec{v_2} = \left(3,~4,~5\right) $ . | 1 |
| 4422 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-1,~4\right) $ and $ \vec{v_2} = \left(0,~2,~-3\right) $ . | 1 |
| 4423 | Find the angle between vectors $ \left(3,~5,~-9\right)$ and $\left(3,~5,~9\right)$. | 1 |
| 4424 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-4\right) $ and $ \vec{v_2} = \left(2,~8,~1\right) $ . | 1 |
| 4425 | Find the difference of the vectors $ \vec{v_1} = \left(944,~-80,~112\right) $ and $ \vec{v_2} = \left(960,~-64,~112\right) $ . | 1 |
| 4426 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-4,~-1\right) $ . | 1 |
| 4427 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-4\right) $ and $ \vec{v_2} = \left(-9,~-5\right) $ . | 1 |
| 4428 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-4\right) $ and $ \vec{v_2} = \left(-8,~-5\right) $ . | 1 |
| 4429 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
| 4430 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 1 |
| 4431 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 4432 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~9\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ . | 1 |
| 4433 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(-3,~0\right) $ . | 1 |
| 4434 | Find the projection of the vector $ \vec{v_1} = \left(6,~-10\right) $ on the vector $ \vec{v_2} = \left(-1,~1\right) $. | 1 |
| 4435 | Calculate the dot product of the vectors $ \vec{v_1} = \left(210,~310\right) $ and $ \vec{v_2} = \left(\dfrac{ 27 }{ 10 },~\dfrac{ 291 }{ 100 }\right) $ . | 1 |
| 4436 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~-9\right) $ and $ \vec{v_2} = \left(6,~-5\right) $ . | 1 |
| 4437 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 7 }{ 25 },~-\dfrac{ 24 }{ 25 }\right) $ . | 1 |
| 4438 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 24 }{ 25 },~-\dfrac{ 7 }{ 25 }\right) $ . | 1 |
| 4439 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~1,~-4\right) $ and $ \vec{v_2} = \left(1,~-2,~2\right) $ . | 1 |
| 4440 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~0\right) $ . | 1 |
| 4441 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-2,~1\right) $ . | 1 |
| 4442 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-2,~1\right) $ and $ \vec{v_2} = \left(1,~-3,~0\right) $ . | 1 |
| 4443 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-4,~5\right) $ . | 1 |
| 4444 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-4,~2\right) $ . | 1 |
| 4445 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4,~-5\right) $ . | 1 |
| 4446 | Find the sum of the vectors $ \vec{v_1} = \left(2,~4,~-5\right) $ and $ \vec{v_2} = \left(1,~2,~3\right) $ . | 1 |
| 4447 | Find the difference of the vectors $ \vec{v_1} = \left(2,~4,~-5\right) $ and $ \vec{v_2} = \left(2,~4,~6\right) $ . | 1 |
| 4448 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~-11\right) $ . | 1 |
| 4449 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~6,~-2\right) $ . | 1 |
| 4450 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~6,~-2\right) $ . | 1 |
