Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2401 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(6,~-1,~4\right)$ are linearly independent or dependent. | 1 |
2402 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~-1\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
2403 | Find the angle between vectors $ \left(-5,~5\right)$ and $\left(3,~6\right)$. | 1 |
2404 | Find the difference of the vectors $ \vec{v_1} = \left(41.4908,~-90.4916\right) $ and $ \vec{v_2} = \left(41.4908,~-90.4914\right) $ . | 1 |
2405 | Determine whether the vectors $ \vec{v_1} = \left(30,~-30,~30\right) $, $ \vec{v_2} = \left(60,~60,~-30\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
2406 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 8 }{ 17 },~\dfrac{ 15 }{ 17 }\right) $ . | 1 |
2407 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~6\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ . | 1 |
2408 | Find the projection of the vector $ \vec{v_1} = \left(0,~\dfrac{ 6 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ on the vector $ \vec{v_2} = \left(-1,~1,~2\right) $. | 1 |
2409 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2,~1\right) $ and $ \vec{v_2} = \left(1,~3,~2\right) $ . | 1 |
2410 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(2,~0,~2\right) $ . | 1 |
2411 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~2,~6\right) $ and $ \vec{v_2} = \left(0,~-8,~3\right) $ . | 1 |
2412 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~1\right) $ . | 1 |
2413 | Find the angle between vectors $ \left(4,~0\right)$ and $\left(5,~-2\right)$. | 1 |
2414 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~9\right) $ and $ \vec{v_2} = \left(7,~2,~1\right) $ . | 1 |
2415 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
2416 | Find the projection of the vector $ \vec{v_1} = \left(-3,~9\right) $ on the vector $ \vec{v_2} = \left(1,~2\right) $. | 1 |
2417 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 27 }{ 10 },~5\right) $ . | 1 |
2418 | 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 |
2419 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\sqrt{ 3 },~-1\right) $ . | 1 |
2420 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-4\right) $ and $ \vec{v_2} = \left(6,~14\right) $ . | 1 |
2421 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~-6\right) $ and $ \vec{v_2} = \left(3,~5,~-6\right) $ . | 1 |
2422 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-2\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ . | 1 |
2423 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~4\right) $ and $ \vec{v_2} = \left(2,~3,~5\right) $ . | 1 |
2424 | Find the sum of the vectors $ \vec{v_1} = \left(8,~1\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 1 |
2425 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~190\right) $ . | 1 |
2426 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(3,~0,~3\right) $ . | 1 |
2427 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-5,~9\right) $ and $ \vec{v_2} = \left(3,~4,~-7\right) $ . | 1 |
2428 | Find the angle between vectors $ \left(4,~4\right)$ and $\left(4,~4\right)$. | 1 |
2429 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~11\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
2430 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0\right) $ . | 1 |
2431 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 8 },~\dfrac{ 5 }{ 8 }\right) $ and $ \vec{v_2} = \left(4,~21\right) $ . | 1 |
2432 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-4,~-2\right) $ and $ \vec{v_2} = \left(8,~-4,~1\right) $ . | 1 |
2433 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~4\right) $ . | 1 |
2434 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(-1,~0,~1\right)$ are linearly independent or dependent. | 1 |
2435 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
2436 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~2\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
2437 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~5\right) $ . | 1 |
2438 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ . | 1 |
2439 | Find the angle between vectors $ \left(4,~3\right)$ and $\left(-1,~5\right)$. | 1 |
2440 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2,~0\right) $ . | 1 |
2441 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~4\right) $, $ \vec{v_2} = \left(2,~3,~5\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
2442 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~12\right) $ . | 1 |
2443 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~7,~-7\right) $ and $ \vec{v_2} = \left(-\dfrac{ 174 }{ 61 },~\dfrac{ 348 }{ 61 },~\dfrac{ 232 }{ 61 }\right) $ . | 1 |
2444 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(3,~0,~3\right) $ . | 1 |
2445 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2,~2\right) $ . | 1 |
2446 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-2\right) $ . | 1 |
2447 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 1 |
2448 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 8 },~\dfrac{ 5 }{ 8 }\right) $ and $ \vec{v_2} = \left(4,~21\right) $ . | 1 |
2449 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~-9\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
2450 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(2,~-3,~8\right)$ are linearly independent or dependent. | 1 |