Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2351 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2\right) $ . | 2 |
2352 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~-24\right) $ . | 2 |
2353 | 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 |
2354 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 2 |
2355 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(7,~1\right)$. | 2 |
2356 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ . | 2 |
2357 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-8,~-4\right) $ . | 2 |
2358 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 347 }{ 100 },~\dfrac{ 197 }{ 10 }\right) $ . | 2 |
2359 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 20 }{ 7 },~-\dfrac{ 25 }{ 7 }\right) $ and $ \vec{v_2} = \left(15,~78\right) $ . | 2 |
2360 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-7\right) $ and $ \vec{v_2} = \left(5,~9\right) $ . | 2 |
2361 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2,~6\right) $ . | 1 |
2362 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~2\right) $ . | 1 |
2363 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~5,~-8\right) $ and $ \vec{v_2} = \left(7,~-2,~3\right) $ . | 1 |
2364 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~2\right) $ and $ \vec{v_2} = \left(-3,~4,~0\right) $ . | 1 |
2365 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-3,~0\right) $ and $ \vec{v_2} = \left(3,~0,~4\right) $ . | 1 |
2366 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1,~-2\right) $ and $ \vec{v_2} = \left(5,~0,~-5\right) $ . | 1 |
2367 | Find the angle between vectors $ \left(1,~-2,~2\right)$ and $\left(-3,~6,~2\right)$. | 1 |
2368 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~4\right) $ and $ \vec{v_2} = \left(2,~\dfrac{ 5 }{ 2 },~0\right) $ . | 1 |
2369 | Find the angle between vectors $ \left(3,~-5\right)$ and $\left(4,~3\right)$. | 1 |
2370 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 7 }{ 25 },~-\dfrac{ 24 }{ 25 }\right) $ . | 1 |
2371 | 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 |
2372 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~-1\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
2373 | Find the sum of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
2374 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~\sqrt{ 3 },~7\right) $ and $ \vec{v_2} = \left(-6,~4,~\sqrt{ 2 }\right) $ . | 1 |
2375 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-3,~6,~-15\right) $ . | 1 |
2376 | Find the projection of the vector $ \vec{v_1} = \left(-1,~2\right) $ on the vector $ \vec{v_2} = \left(1,~-1\right) $. | 1 |
2377 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(2,~2,~2\right) $ . | 1 |
2378 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~4,~0\right) $ and $ \vec{v_2} = \left(0,~3,~-3\right) $ . | 1 |
2379 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 1 |
2380 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-3,~0\right) $ and $ \vec{v_2} = \left(3,~0,~4\right) $ . | 1 |
2381 | Find the angle between vectors $ \left(4,~-4\right)$ and $\left(-4,~-4\right)$. | 1 |
2382 | Find the angle between vectors $ \left(1,~-2,~2\right)$ and $\left(4,~5,~3\right)$. | 1 |
2383 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-6\right) $ . | 1 |
2384 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(9,~22\right) $ . | 1 |
2385 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(4,~12,~0\right) $ . | 1 |
2386 | 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 |
2387 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-4,~1\right) $ and $ \vec{v_2} = \left(0,~8,~-8\right) $ . | 1 |
2388 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
2389 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~5\right) $ and $ \vec{v_2} = \left(3,~6\right) $ . | 1 |
2390 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-8,~-4\right) $ and $ \vec{v_2} = \left(-1,~-4,~-4\right) $ . | 1 |
2391 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 8 }{ 17 },~\dfrac{ 15 }{ 17 }\right) $ and $ \vec{v_2} = \left(15,~78\right) $ . | 1 |
2392 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~3,~-2\right) $ and $ \vec{v_2} = \left(-2,~5,~2\right) $ . | 1 |
2393 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(3,~0\right) $ . | 1 |
2394 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-9,~2,~7\right) $ and $ \vec{v_2} = \left(3,~-7,~0\right) $ . | 1 |
2395 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-62,~-39\right) $ and $ \vec{v_2} = \left(8,~2,~-1\right) $ . | 1 |
2396 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-5,~1\right) $ . | 1 |
2397 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-50,~4\right) $ . | 1 |
2398 | Find the difference of the vectors $ \vec{v_1} = \left(-8,~6\right) $ and $ \vec{v_2} = \left(-6,~2\right) $ . | 1 |
2399 | Find the angle between vectors $ \left(1,~-2,~2\right)$ and $\left(-2,~4,~-4\right)$. | 1 |
2400 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 24 }{ 25 },~-\dfrac{ 7 }{ 25 }\right) $ . | 1 |