Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2451 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-2\right) $ and $ \vec{v_2} = \left(5,~-5\right) $ . | 1 |
| 2452 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-6\right) $ and $ \vec{v_2} = \left(7,~4\right) $ . | 1 |
| 2453 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-5\right) $ and $ \vec{v_2} = \left(3,~6\right) $ . | 1 |
| 2454 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3\right) $ . | 1 |
| 2455 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-8,~4\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 2456 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~5,~-1\right) $ and $ \vec{v_2} = \left(-5,~-1,~1\right) $ . | 1 |
| 2457 | Find the angle between vectors $ \left(1,~5,~-1\right)$ and $\left(-5,~-1,~1\right)$. | 1 |
| 2458 | Find the angle between vectors $ \left(5,~-1,~1\right)$ and $\left(-5,~-1,~1\right)$. | 1 |
| 2459 | Find the angle between vectors $ \left(-5,~-1,~1\right)$ and $\left(-1,~1,~5\right)$. | 1 |
| 2460 | Find the angle between vectors $ \left(5,~-1,~1\right)$ and $\left(-1,~1,~5\right)$. | 1 |
| 2461 | Find the angle between vectors $ \left(-1,~-1,~5\right)$ and $\left(-1,~1,~4\right)$. | 1 |
| 2462 | Find the angle between vectors $ \left(1,~5,~-1\right)$ and $\left(-5,~-1,~1\right)$. | 1 |
| 2463 | Find the angle between vectors $ \left(-5,~-1,~1\right)$ and $\left(-1,~-1,~5\right)$. | 1 |
| 2464 | Find the angle between vectors $ \left(5,~-1,~1\right)$ and $\left(-1,~-1,~5\right)$. | 1 |
| 2465 | Find the sum of the vectors $ \vec{v_1} = \left(1,~5\right) $ and $ \vec{v_2} = \left(9,~1\right) $ . | 1 |
| 2466 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 2467 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\sqrt{ 2 },~-\sqrt{ 3 }\right) $ . | 1 |
| 2468 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-2,~-5\right) $ . | 1 |
| 2469 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-7,~3\right) $ and $ \vec{v_2} = \left(0,~1,~\dfrac{ 7 }{ 3 }\right) $ . | 1 |
| 2470 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-7,~3\right) $ and $ \vec{v_2} = \left(0,~1,~\dfrac{ 7 }{ 3 }\right) $ . | 1 |
| 2471 | Find the projection of the vector $ \vec{v_1} = \left(-7,~4\right) $ on the vector $ \vec{v_2} = \left(-1,~-4\right) $. | 1 |
| 2472 | Find the projection of the vector $ \vec{v_1} = \left(2,~0\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 1 |
| 2473 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 1 |
| 2474 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ . | 1 |
| 2475 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-4\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 1 |
| 2476 | Find the angle between vectors $ \left(-15,~-8\right)$ and $\left(-2,~3\right)$. | 1 |
| 2477 | Find the angle between vectors $ \left(-3,~4\right)$ and $\left(2,~3\right)$. | 1 |
| 2478 | Determine whether the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-9,~3\right) $ are linearly independent or dependent. | 1 |
| 2479 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 27 }{ 10 },~5\right) $ . | 1 |
| 2480 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~7\right) $ . | 1 |
| 2481 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-4\right) $ . | 1 |
| 2482 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(1,~4,~3\right) $ . | 1 |
| 2483 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~3\right) $ . | 1 |
| 2484 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-6\right) $ . | 1 |
| 2485 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1.5,~0,~3\right) $ and $ \vec{v_2} = \left(0,~2.6,~1.5\right) $ . | 1 |
| 2486 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~2\right) $ and $ \vec{v_2} = \left(0,~2.6,~1.5\right) $ . | 1 |
| 2487 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1.5,~0,~3\right) $ and $ \vec{v_2} = \left(-7.79,~-2.25,~3.9\right) $ . | 1 |
| 2488 | Find the angle between vectors $ \left(-13,~24\right)$ and $\left(-\dfrac{ 50303 }{ 5000 },~\dfrac{ 50303 }{ 5000 }\right)$. | 1 |
| 2489 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~14\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 2490 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~6\right) $ and $ \vec{v_2} = \left(0,~4.24,~4.24\right) $ . | 1 |
| 2491 | Find the projection of the vector $ \vec{v_1} = \left(-5,~12\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 1 |
| 2492 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(4,~5,~6\right) $ . | 1 |
| 2493 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(0,~-4\right) $ . | 1 |
| 2494 | Find the projection of the vector $ \vec{v_1} = \left(-5,~3\right) $ on the vector $ \vec{v_2} = \left(-1,~-1\right) $. | 1 |
| 2495 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-10,~0\right) $ and $ \vec{v_2} = \left(0,~-1.688,~4.24\right) $ . | 1 |
| 2496 | Find the angle between vectors $ \left(8,~-4,~7\right)$ and $\left(40,~-20,~35\right)$. | 1 |
| 2497 | Determine whether the vectors $ \vec{v_1} = \left(0,~0,~1\right) $, $ \vec{v_2} = \left(1,~2,~1\right) $ and $ \vec{v_3} = \left(0,~1,~1\right)$ are linearly independent or dependent. | 1 |
| 2498 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~1\right) $ . | 1 |
| 2499 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 10 },~\dfrac{ 9 }{ 10 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ . | 1 |
| 2500 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 173 }{ 100 },~1\right) $ and $ \vec{v_2} = \left(-\dfrac{ 173 }{ 50 },~2\right) $ . | 1 |
