Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6351 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-5\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
6352 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~4,~2\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 1 |
6353 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~2\right) $ . | 1 |
6354 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ . | 1 |
6355 | Find the angle between vectors $ \left(5,~-5\right)$ and $\left(5,~\dfrac{ 501 }{ 100 }\right)$. | 1 |
6356 | Find the projection of the vector $ \vec{v_1} = \left(2,~4\right) $ on the vector $ \vec{v_2} = \left(5,~6\right) $. | 1 |
6357 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $ and $ \vec{v_2} = \left(4,~5,~-6\right) $ . | 1 |
6358 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~2,~-3\right) $ and $ \vec{v_2} = \left(3,~-2,~2\right) $ . | 1 |
6359 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-\sqrt{ 3 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\sqrt{ 2 },~1,~\dfrac{ 2 }{ 3 }\right) $ . | 1 |
6360 | Find the difference of the vectors $ \vec{v_1} = \left(6,~8,~4\right) $ and $ \vec{v_2} = \left(8,~5,~7\right) $ . | 1 |
6361 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~3\right) $ on the vector $ \vec{v_2} = \left(0,~1,~4\right) $. | 1 |
6362 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(0,~-3,~2\right) $ . | 1 |
6363 | Find the angle between vectors $ \left(6,~4\right)$ and $\left(5,~8\right)$. | 1 |
6364 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-5,~-7\right) $ . | 1 |
6365 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~6,~3\right) $ and $ \vec{v_2} = \left(3,~3,~-2\right) $ . | 1 |
6366 | Find the difference of the vectors $ \vec{v_1} = \left(-109914,~75574,~4614\right) $ and $ \vec{v_2} = \left(-118365,~77821,~5275\right) $ . | 1 |
6367 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~-1\right) $ . | 1 |
6368 | Find the projection of the vector $ \vec{v_1} = \left(-6,~3\right) $ on the vector $ \vec{v_2} = \left(-1,~1\right) $. | 1 |
6369 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
6370 | Find the angle between vectors $ \left(5,~-5\right)$ and $\left(\dfrac{ 501 }{ 100 },~5\right)$. | 1 |
6371 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~25\right) $ . | 1 |
6372 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 1 |
6373 | 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 |
6374 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-3\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ . | 1 |
6375 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~4\right) $ and $ \vec{v_2} = \left(4,~5,~3\right) $ . | 1 |
6376 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(0,~1,~4\right)$. | 1 |
6377 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~2,~2\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
6378 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~5\right) $ . | 1 |
6379 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(3,~-3\right) $ . | 1 |
6380 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 1 |
6381 | Find the magnitude of the vector $ \| \vec{v} \| = \left(89,~157\right) $ . | 1 |
6382 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-15\right) $ . | 1 |
6383 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 73 }{ 1000 },~0,~0\right) $ . | 1 |
6384 | 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 |
6385 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4,~0\right) $ . | 1 |
6386 | Find the sum of the vectors $ \vec{v_1} = \left(5,~5\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 1 |
6387 | 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 |
6388 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~6\right) $ . | 1 |
6389 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~2\right) $ and $ \vec{v_2} = \left(1,~-1,~-2\right) $ . | 1 |
6390 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~10,~-6\right) $ . | 1 |
6391 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-64,~-3,~33\right) $ and $ \vec{v_2} = \left(0,~-3,~2\right) $ . | 1 |
6392 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-4,~-1,~2\right) $ . | 1 |
6393 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
6394 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8451,~-2247,~-661\right) $ . | 1 |
6395 | Find the angle between vectors $ \left(-1,~25\right)$ and $\left(41,~1\right)$. | 1 |
6396 | 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 |
6397 | Find the angle between vectors $ \left(-3,~-1\right)$ and $\left(3,~3\right)$. | 1 |
6398 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~8,~9\right) $ and $ \vec{v_2} = \left(6,~-4,~5\right) $ . | 1 |
6399 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-0.5614,~0.5614,~0\right) $ . | 1 |
6400 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~0\right) $ and $ \vec{v_2} = \left(1,~8\right) $ . | 1 |