Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1451 | Find the difference of the vectors $ \vec{v_1} = \left(2,~7\right) $ and $ \vec{v_2} = \left(6,~3\right) $ . | 2 |
1452 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 2 |
1453 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 100493 }{ 1000 },~-\dfrac{ 1419 }{ 500 }\right) $ . | 2 |
1454 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 2 |
1455 | Find the angle between vectors $ \left(\sqrt{ 3 },~-7,~0\right)$ and $\left(\sqrt{ 3 },~1,~-2\right)$. | 2 |
1456 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(-8,~5\right) $ . | 2 |
1457 | Find the angle between vectors $ \left(1,~0,~0\right)$ and $\left(-1,~0,~1\right)$. | 2 |
1458 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-1\right) $ . | 2 |
1459 | Find the angle between vectors $ \left(-15,~-8\right)$ and $\left(-1,~9\right)$. | 2 |
1460 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-3\right) $ and $ \vec{v_2} = \left(-5,~7\right) $ . | 2 |
1461 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-10,~20\right) $ . | 2 |
1462 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ . | 2 |
1463 | Find the magnitude of the vector $ \| \vec{v} \| = \left(32,~8\right) $ . | 2 |
1464 | Find the sum of the vectors $ \vec{v_1} = \left(8,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 529919 }{ 100000 },~\dfrac{ 53003 }{ 6250 }\right) $ . | 2 |
1465 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(-8,~1,~2\right)$. | 2 |
1466 | Find the angle between vectors $ \left(5,~-1,~1\right)$ and $\left(-1,~1,~4\right)$. | 2 |
1467 | Find the sum of the vectors $ \vec{v_1} = \left(4,~8\right) $ and $ \vec{v_2} = \left(4,~-7\right) $ . | 2 |
1468 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~10\right) $ and $ \vec{v_2} = \left(-\dfrac{ 3 }{ 2 },~\dfrac{ 3 }{ 5 }\right) $ . | 2 |
1469 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 46 }{ 5 },~\dfrac{ 71 }{ 10 }\right) $ . | 2 |
1470 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~11,~10\right) $ . | 2 |
1471 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~-3\right) $ . | 2 |
1472 | Find the sum of the vectors $ \vec{v_1} = \left(8,~3\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ . | 2 |
1473 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3,~1\right) $ . | 2 |
1474 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 2 |
1475 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~4\right) $ . | 2 |
1476 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~\sqrt{ 29 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 2 |
1477 | Find the magnitude of the vector $ \| \vec{v} \| = \left(34,~16\right) $ . | 2 |
1478 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 2 |
1479 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~5\right) $ and $ \vec{v_2} = \left(-3,~9\right) $ . | 2 |
1480 | Find the angle between vectors $ \left(3,~-2\right)$ and $\left(-1,~5\right)$. | 2 |
1481 | Determine whether the vectors $ \vec{v_1} = \left(1,~1,~0\right) $, $ \vec{v_2} = \left(1,~2,~1\right) $ and $ \vec{v_3} = \left(0,~1,~1\right)$ are linearly independent or dependent. | 2 |
1482 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-4,~0\right) $ and $ \vec{v_2} = \left(-3,~8,~0\right) $ . | 2 |
1483 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~6\right) $ . | 2 |
1484 | Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(5,~0\right) $ . | 2 |
1485 | Determine whether the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-4,~0\right) $ are linearly independent or dependent. | 2 |
1486 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~-8\right) $ . | 2 |
1487 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 2 |
1488 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 14 }{ 5 },~\dfrac{ 123 }{ 5 }\right) $ . | 2 |
1489 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 2 |
1490 | Determine whether the vectors $ \vec{v_1} = \left(0,~0,~0\right) $, $ \vec{v_2} = \left(0,~0,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 2 |
1491 | Find the angle between vectors $ \left(4,~2\right)$ and $\left(1,~-2\right)$. | 2 |
1492 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 21 }{ 10 },~-\dfrac{ 16 }{ 5 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 2 |
1493 | Find the sum of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 2 |
1494 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 13271 }{ 1000 },~-\dfrac{ 773789 }{ 10000 }\right) $ . | 2 |
1495 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~-6,~9\right) $ and $ \vec{v_2} = \left(5,~-3,~4\right) $ . | 2 |
1496 | Find the sum of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 2 |
1497 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 2 |
1498 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-5\right) $ . | 2 |
1499 | Find the sum of the vectors $ \vec{v_1} = \left(2,~7\right) $ and $ \vec{v_2} = \left(8,~0\right) $ . | 2 |
1500 | Find the angle between vectors $ \left(9,~-7\right)$ and $\left(-10,~7\right)$. | 2 |