Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1501 | Find the angle between vectors $ \left(-7,~8\right)$ and $\left(1,~0\right)$. | 2 |
1502 | Determine whether the vectors $ \vec{v_1} = \left(3,~12,~-21\right) $, $ \vec{v_2} = \left(2,~-1,~4\right) $ and $ \vec{v_3} = \left(0,~-10,~20\right)$ are linearly independent or dependent. | 2 |
1503 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 2 |
1504 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 2 |
1505 | Determine whether the vectors $ \vec{v_1} = \left(0,~-32\right) $ and $ \vec{v_2} = \left(6,~-185\right) $ are linearly independent or dependent. | 2 |
1506 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 2 |
1507 | Find the difference of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 2 |
1508 | Find the sum of the vectors $ \vec{v_1} = \left(5.2094,~29.5442\right) $ and $ \vec{v_2} = \left(-20,~-34.641\right) $ . | 2 |
1509 | Find the difference of the vectors $ \vec{v_1} = \left(5,~6\right) $ and $ \vec{v_2} = \left(-4,~-1\right) $ . | 2 |
1510 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~1\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 2 |
1511 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 2 |
1512 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ . | 2 |
1513 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~5\right) $ . | 2 |
1514 | Find the projection of the vector $ \vec{v_1} = \left(15.898,~25.441\right) $ on the vector $ \vec{v_2} = \left(6.84,~18.79\right) $. | 2 |
1515 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(2,~-\dfrac{ 1 }{ 4 }\right) $ . | 2 |
1516 | Determine whether the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(-1,~0\right) $ are linearly independent or dependent. | 2 |
1517 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~10\right) $ and $ \vec{v_2} = \left(5,~7\right) $ . | 2 |
1518 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-1\right) $ . | 2 |
1519 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 2 |
1520 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-9\right) $ . | 2 |
1521 | Find the angle between vectors $ \left(0,~-32\right)$ and $\left(6,~-185\right)$. | 2 |
1522 | Find the angle between vectors $ \left(1,~-2,~-1\right)$ and $\left(1,~0,~-1\right)$. | 2 |
1523 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-3,~8\right) $ . | 2 |
1524 | Determine whether the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ are linearly independent or dependent. | 2 |
1525 | Find the angle between vectors $ \left(7,~4\right)$ and $\left(-4,~7\right)$. | 2 |
1526 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ . | 2 |
1527 | Calculate the dot product of the vectors $ \vec{v_1} = \left(100,~200,~-50\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 2 |
1528 | Find the difference of the vectors $ \vec{v_1} = \left(6,~6,~6\right) $ and $ \vec{v_2} = \left(1,~-1,~1\right) $ . | 2 |
1529 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 2 |
1530 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
1531 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~7\right) $ . | 2 |
1532 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(6,~-4\right) $ . | 2 |
1533 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~6\right) $ and $ \vec{v_2} = \left(-25.44,~-13.36,~20.44\right) $ . | 2 |
1534 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-2\right) $ . | 2 |
1535 | Find the sum of the vectors $ \vec{v_1} = \left(-10,~12\right) $ and $ \vec{v_2} = \left(5,~-10\right) $ . | 2 |
1536 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-1\right) $ . | 2 |
1537 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~10\right) $ and $ \vec{v_2} = \left(5,~7\right) $ . | 2 |
1538 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-10,~5\right) $ . | 2 |
1539 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(5,~4\right) $ . | 2 |
1540 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~3\right) $ . | 2 |
1541 | Find the projection of the vector $ \vec{v_1} = \left(-10,~-4\right) $ on the vector $ \vec{v_2} = \left(4,~-3\right) $. | 2 |
1542 | Find the difference of the vectors $ \vec{v_1} = \left(10,~10\right) $ and $ \vec{v_2} = \left(21,~21\right) $ . | 2 |
1543 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 55651 }{ 10000 },~\dfrac{ 5327 }{ 625 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 13 }{ 2 },~-11.2583\right) $ . | 2 |
1544 | Find the angle between vectors $ \left(-3,~10\right)$ and $\left(5,~7\right)$. | 2 |
1545 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-4\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 2 |
1546 | Find the magnitude of the vector $ \| \vec{v} \| = \left(- \dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right) $ . | 2 |
1547 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~4\right) $ . | 2 |
1548 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(1,~\dfrac{ 1 }{ 4 }\right) $ . | 2 |
1549 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~6\right) $ . | 2 |
1550 | Find the angle between vectors $ \left(3,~-4\right)$ and $\left(-5,~-12\right)$. | 2 |