Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2551 | 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 |
| 2552 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~2\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
| 2553 | Determine whether the vectors $ \vec{v_1} = \left(8,~-4\right) $ and $ \vec{v_2} = \left(5,~10\right) $ are linearly independent or dependent. | 1 |
| 2554 | Find the angle between vectors $ \left(8,~-4\right)$ and $\left(5,~10\right)$. | 1 |
| 2555 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 3 },~-\dfrac{ 3 }{ 2 }\right)$ and $\left(-4,~18\right)$. | 1 |
| 2556 | Find the angle between vectors $ \left(1,~-3\right)$ and $\left(-4,~3\right)$. | 1 |
| 2557 | Find the magnitude of the vector $ \| \vec{v} \| = \left(52,~-7\right) $ . | 1 |
| 2558 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~-3\right) $ . | 1 |
| 2559 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 1 |
| 2560 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~3\right) $ . | 1 |
| 2561 | Find the angle between vectors $ \left(1,~3\right)$ and $\left(3,~-2\right)$. | 1 |
| 2562 | Find the difference of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(0,~2\right) $ . | 1 |
| 2563 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(0,~4\right) $ . | 1 |
| 2564 | Find the angle between vectors $ \left(-\dfrac{ 46 }{ 5 },~-\dfrac{ 22 }{ 5 },~-\dfrac{ 6 }{ 5 }\right)$ and $\left(-\dfrac{ 44 }{ 5 },~\dfrac{ 67 }{ 10 },~\dfrac{ 27 }{ 10 }\right)$. | 1 |
| 2565 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 83 }{ 10 },~\dfrac{ 27 }{ 10 },~\dfrac{ 27 }{ 10 }\right) $ and $ \vec{v_2} = \left(-3,~\dfrac{ 33 }{ 5 },~\dfrac{ 31 }{ 10 }\right) $ . | 1 |
| 2566 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 1 |
| 2567 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(3,~-4\right) $ . | 1 |
| 2568 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 48 }{ 5 },~-\dfrac{ 97 }{ 10 },~-\dfrac{ 23 }{ 5 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 49 }{ 10 },~-\dfrac{ 15 }{ 2 },~\dfrac{ 37 }{ 5 }\right) $ . | 1 |
| 2569 | Find the projection of the vector $ \vec{v_1} = \left(-24,~7\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 1 |
| 2570 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-15,~8\right) $ . | 1 |
| 2571 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-6,~-\dfrac{ 21 }{ 5 },~-\dfrac{ 37 }{ 5 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 15 }{ 2 },~\dfrac{ 3 }{ 2 },~\dfrac{ 23 }{ 10 }\right) $ . | 1 |
| 2572 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ . | 1 |
| 2573 | Find the angle between vectors $ \left(-12,~-5\right)$ and $\left(-2,~5\right)$. | 1 |
| 2574 | Find the angle between vectors $ \left(-3,~4\right)$ and $\left(8,~3\right)$. | 1 |
| 2575 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 36 }{ 25 },~\dfrac{ 693 }{ 10 },~\dfrac{ 81 }{ 2 }\right) $ . | 1 |
| 2576 | Find the angle between vectors $ \left(\dfrac{ 23 }{ 5 },~-\dfrac{ 41 }{ 5 },~\dfrac{ 49 }{ 5 }\right)$ and $\left(-9,~-\dfrac{ 33 }{ 10 },~\dfrac{ 22 }{ 5 }\right)$. | 1 |
| 2577 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1.5,~0,~3\right) $ and $ \vec{v_2} = \left(0,~2.6,~2.6\right) $ . | 1 |
| 2578 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1.5,~0,~3\right) $ and $ \vec{v_2} = \left(-7.8,~-3.9,~3.9\right) $ . | 1 |
| 2579 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~4.5,~2\right) $ and $ \vec{v_2} = \left(0,~2.6,~1.5\right) $ . | 1 |
| 2580 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~7\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 1 |
| 2581 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~0\right) $ and $ \vec{v_2} = \left(-25.44,~-13.36,~20.44\right) $ . | 1 |
| 2582 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~6\right) $ and $ \vec{v_2} = \left(-25.44,~-13.36,~20.44\right) $ . | 1 |
| 2583 | Determine whether the vectors $ \vec{v_1} = \left(4,~9\right) $ and $ \vec{v_2} = \left(-8,~-18\right) $ are linearly independent or dependent. | 1 |
| 2584 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3 \sqrt{ 3 },~3\right) $ . | 1 |
| 2585 | Find the sum of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(7,~2\right) $ . | 1 |
| 2586 | Find the sum of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(7,~3\right) $ . | 1 |
| 2587 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(7,~2\right) $ . | 1 |
| 2588 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 129 }{ 25 },~-\dfrac{ 203 }{ 50 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 361 }{ 100 },~0,~-\dfrac{ 173 }{ 100 }\right) $ . | 1 |
| 2589 | Find the difference of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 129 }{ 25 },~-\dfrac{ 203 }{ 50 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 361 }{ 100 },~0,~-\dfrac{ 173 }{ 100 }\right) $ . | 1 |
| 2590 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 361 }{ 100 },~\dfrac{ 129 }{ 25 },~-\dfrac{ 233 }{ 100 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 379 }{ 100 },~0,~-\dfrac{ 561 }{ 100 }\right) $ . | 1 |
| 2591 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 361 }{ 100 },~\dfrac{ 129 }{ 25 },~-\dfrac{ 233 }{ 100 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 379 }{ 100 },~0,~-\dfrac{ 561 }{ 100 }\right) $ . | 1 |
| 2592 | 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 |
| 2593 | 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(-\dfrac{ 463 }{ 100 },~0,~\dfrac{ 463 }{ 100 }\right) $ . | 1 |
| 2594 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 29 }{ 10 },~0,~-\dfrac{ 29 }{ 10 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 463 }{ 100 },~0,~\dfrac{ 463 }{ 100 }\right) $ . | 1 |
| 2595 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 29 }{ 10 },~0,~-\dfrac{ 29 }{ 10 }\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 217 }{ 25 },~0\right) $ . | 1 |
| 2596 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 1 |
| 2597 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~4\right) $ . | 1 |
| 2598 | Find the difference of the vectors $ \vec{v_1} = \left(7,~7\right) $ and $ \vec{v_2} = \left(\dfrac{ 14 }{ 5 },~\dfrac{ 42 }{ 5 }\right) $ . | 1 |
| 2599 | Find the difference of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(\dfrac{ 22 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ . | 1 |
| 2600 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-4\right) $ . | 1 |
