Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6501 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-4\right) $ and $ \vec{v_2} = \left(6,~-2\right) $ . | 1 |
6502 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~3,~1\right) $ and $ \vec{v_2} = \left(6,~3,~1\right) $ . | 1 |
6503 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~0\right) $ and $ \vec{v_2} = \left(3,~-1,~2\right) $ . | 1 |
6504 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~0,~-1\right) $ . | 1 |
6505 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~2,~0\right) $ . | 1 |
6506 | Find the magnitude of the vector $ \| \vec{v} \| = \left(20,~-15,~0\right) $ . | 1 |
6507 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(2,~8\right) $ . | 1 |
6508 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~7,~-2\right) $ and $ \vec{v_2} = \left(6,~1,~-4\right) $ . | 1 |
6509 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-5\right) $ . | 1 |
6510 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(-3,~1\right) $ . | 1 |
6511 | Find the projection of the vector $ \vec{v_1} = \left(2,~2\right) $ on the vector $ \vec{v_2} = \left(4,~-5\right) $. | 1 |
6512 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 1 |
6513 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(-4,~3\right)$. | 1 |
6514 | Find the sum of the vectors $ \vec{v_1} = \left(6,~9,~3\right) $ and $ \vec{v_2} = \left(2,~6,~0\right) $ . | 1 |
6515 | Find the angle between vectors $ \left(-2,~5\right)$ and $\left(9,~8\right)$. | 1 |
6516 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~8\right) $ . | 1 |
6517 | Find the sum of the vectors $ \vec{v_1} = \left(4,~18\right) $ and $ \vec{v_2} = \left(30,~-20\right) $ . | 1 |
6518 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
6519 | Determine whether the vectors $ \vec{v_1} = \left(2,~-2,~4\right) $, $ \vec{v_2} = \left(-1,~2,~3\right) $ and $ \vec{v_3} = \left(3,~6,~11\right)$ are linearly independent or dependent. | 1 |
6520 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~\dfrac{ 7 }{ 2 },~-\dfrac{ 49 }{ 10 }\right) $ . | 1 |
6521 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 1 |
6522 | Find the angle between vectors $ \left(4,~6,~-3\right)$ and $\left(-2,~3,~-4\right)$. | 1 |
6523 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-2\right) $ and $ \vec{v_2} = \left(5,~-5\right) $ . | 1 |
6524 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 29 }{ 10 },~\dfrac{ 129 }{ 25 },~-\dfrac{ 29 }{ 10 }\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 217 }{ 25 },~0\right) $ . | 1 |
6525 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1,~-1\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
6526 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~-4\right) $ and $ \vec{v_2} = \left(3,~-4,~5\right) $ . | 1 |
6527 | Find the difference of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(6,~-7\right) $ . | 1 |
6528 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~-6\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
6529 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(4,~1\right)$. | 1 |
6530 | Find the difference of the vectors $ \vec{v_1} = \left(-9,~3\right) $ and $ \vec{v_2} = \left(-3,~9\right) $ . | 1 |
6531 | Find the angle between vectors $ \left(7,~2,~-2\right)$ and $\left(6,~-3,~0\right)$. | 1 |
6532 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~6\right) $ and $ \vec{v_2} = \left(2,~2,~6\right) $ . | 1 |
6533 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(4,~-4,~1\right) $ . | 1 |
6534 | Find the angle between vectors $ \left(5,~-5,~-4\right)$ and $\left(3,~-4,~-1\right)$. | 1 |
6535 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~1,~2\right) $ and $ \vec{v_2} = \left(1,~2,~0\right) $ . | 1 |
6536 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~15\right) $ . | 1 |
6537 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~-5\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 1 |
6538 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $, $ \vec{v_2} = \left(1,~1,~2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
6539 | Find the angle between vectors $ \left(-1,~9\right)$ and $\left(5,~2\right)$. | 1 |
6540 | Determine whether the vectors $ \vec{v_1} = \left(2,~-2,~4\right) $, $ \vec{v_2} = \left(-1,~2,~3\right) $ and $ \vec{v_3} = \left(-1,~2,~4\right)$ are linearly independent or dependent. | 1 |
6541 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-6\right) $ and $ \vec{v_2} = \left(7,~4\right) $ . | 1 |
6542 | Find the difference of the vectors $ \vec{v_1} = \left(-24,~21\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ . | 1 |
6543 | Find the projection of the vector $ \vec{v_1} = \left(1,~-6\right) $ on the vector $ \vec{v_2} = \left(2,~-1\right) $. | 1 |
6544 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~6\right) $ and $ \vec{v_2} = \left(2,~2,~6\right) $ . | 1 |
6545 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-4,~1\right) $ and $ \vec{v_2} = \left(4,~-1,~-5\right) $ . | 1 |
6546 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~4\right) $ . | 1 |
6547 | Find the angle between vectors $ \left(4,~4\right)$ and $\left(-4,~-4\right)$. | 1 |
6548 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~5,~3\right) $ and $ \vec{v_2} = \left(4,~-4,~3\right) $ . | 1 |
6549 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(6,~-3\right) $ . | 1 |
6550 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-5\right) $ and $ \vec{v_2} = \left(3,~6\right) $ . | 1 |