Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2351 | Find the angle between vectors $ \left(2,~0\right)$ and $\left(-2,~-1\right)$. | 2 |
| 2352 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ . | 2 |
| 2353 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ . | 2 |
| 2354 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ . | 2 |
| 2355 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 2 |
| 2356 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 8119 }{ 3125 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(-5,~0\right) $ . | 2 |
| 2357 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1\right) $ . | 2 |
| 2358 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 2 |
| 2359 | Determine whether the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ are linearly independent or dependent. | 2 |
| 2360 | Determine whether the vectors $ \vec{v_1} = \left(-1,~2,~4\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(-3,~0,~5\right)$ are linearly independent or dependent. | 1 |
| 2361 | Determine whether the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(1,~2\right) $ are linearly independent or dependent. | 1 |
| 2362 | Determine whether the vectors $ \vec{v_1} = \left(0,~-1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent. | 1 |
| 2363 | Determine whether the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(1,~-7,~11\right)$ are linearly independent or dependent. | 1 |
| 2364 | Determine whether the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(1,~-1,~0\right)$ are linearly independent or dependent. | 1 |
| 2365 | Determine whether the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(1,~2,~3\right)$ are linearly independent or dependent. | 1 |
| 2366 | Determine whether the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(4,~-3,~4\right)$ are linearly independent or dependent. | 1 |
| 2367 | 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,~2,~5\right)$ are linearly independent or dependent. | 1 |
| 2368 | 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 |
| 2369 | 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 |
| 2370 | 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(5,~2,~5\right)$ are linearly independent or dependent. | 1 |
| 2371 | 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 |
| 2372 | 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 |
| 2373 | 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 |
| 2374 | 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,~2,~1\right)$ are linearly independent or dependent. | 1 |
| 2375 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~3,~5\right) $ . | 1 |
| 2376 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~3\right) $, $ \vec{v_2} = \left(1,~3,~5\right) $ and $ \vec{v_3} = \left(2,~5,~8\right)$ are linearly independent or dependent. | 1 |
| 2377 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 1 |
| 2378 | Find the angle between vectors $ \left(-5,~7\right)$ and $\left(-1,~-3\right)$. | 1 |
| 2379 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(8,~-16\right) $ . | 1 |
| 2380 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 186 }{ 5 },~0\right) $ . | 1 |
| 2381 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(10,~4\right) $ . | 1 |
| 2382 | Find the projection of the vector $ \vec{v_1} = \left(-4,~7\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 1 |
| 2383 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-3\right) $ . | 1 |
| 2384 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(3,~-4\right) $ . | 1 |
| 2385 | Find the sum of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
| 2386 | Determine whether the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ are linearly independent or dependent. | 1 |
| 2387 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-3\right) $ . | 1 |
| 2388 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~3\right) $ and $ \vec{v_2} = \left(-5,~4\right) $ . | 1 |
| 2389 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-12,~9\right) $ . | 1 |
| 2390 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~4\right) $ . | 1 |
| 2391 | Find the angle between vectors $ \left(2,~0\right)$ and $\left(0,~-7\right)$. | 1 |
| 2392 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 1 |
| 2393 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-1\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ . | 1 |
| 2394 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4,~0\right) $ . | 1 |
| 2395 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~0\right) $ and $ \vec{v_2} = \left(1,~1,~-1\right) $ . | 1 |
| 2396 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~\dfrac{ 7 }{ 2 },~-\dfrac{ 49 }{ 10 }\right) $ . | 1 |
| 2397 | 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 |
| 2398 | 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 |
| 2399 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(2,~3,~3\right) $ . | 1 |
| 2400 | 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(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
