Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6301 | Find the sum of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(4,~4\right) $ . | 1 |
| 6302 | Find the angle between vectors $ \left(1,~2\right)$ and $\left(4,~7\right)$. | 1 |
| 6303 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 1 |
| 6304 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(-6,~1\right) $ . | 1 |
| 6305 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 1 |
| 6306 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-6\right) $ and $ \vec{v_2} = \left(-1,~-2\right) $ . | 1 |
| 6307 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~0\right) $ and $ \vec{v_2} = \left(1,~-4\right) $ . | 1 |
| 6308 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-4\right) $ and $ \vec{v_2} = \left(-6,~-1\right) $ . | 1 |
| 6309 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~24\right) $ and $ \vec{v_2} = \left(-5,~-12\right) $ . | 1 |
| 6310 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 1 |
| 6311 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~\dfrac{ 5919 }{ 20 }\right) $ . | 1 |
| 6312 | Find the angle between vectors $ \left(0,~\dfrac{ 5919 }{ 20 }\right)$ and $\left(0,~-\dfrac{ 147 }{ 20 }\right)$. | 1 |
| 6313 | Find the angle between vectors $ \left(6,~2\right)$ and $\left(-4,~3\right)$. | 1 |
| 6314 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ . | 1 |
| 6315 | Find the angle between vectors $ \left(-5,~8\right)$ and $\left(-4,~8\right)$. | 1 |
| 6316 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~1\right) $ . | 1 |
| 6317 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ are linearly independent or dependent. | 1 |
| 6318 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-2,~4\right) $ and $ \vec{v_2} = \left(4,~4,~0\right) $ . | 1 |
| 6319 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~9\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 1 |
| 6320 | Determine whether the vectors $ \vec{v_1} = \left(-3,~-6\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ are linearly independent or dependent. | 1 |
| 6321 | Find the angle between vectors $ \left(2,~4\right)$ and $\left(4,~-2\right)$. | 1 |
| 6322 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-45\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 1 |
| 6323 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(0,~5\right) $ . | 1 |
| 6324 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 1 |
| 6325 | Find the sum of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(4,~-6\right) $ . | 1 |
| 6326 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 6327 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 1 |
| 6328 | Find the difference of the vectors $ \vec{v_1} = \left(6,~4,~9\right) $ and $ \vec{v_2} = \left(5,~7,~2\right) $ . | 1 |
| 6329 | Find the difference of the vectors $ \vec{v_1} = \left(132252,~20000,~15999\right) $ and $ \vec{v_2} = \left(130182,~20111,~15419\right) $ . | 1 |
| 6330 | Find the difference of the vectors $ \vec{v_1} = \left(132163,~20000,~15950\right) $ and $ \vec{v_2} = \left(130182,~20000,~15419\right) $ . | 1 |
| 6331 | Find the difference of the vectors $ \vec{v_1} = \left(132163,~20000,~15950\right) $ and $ \vec{v_2} = \left(131506,~20869,~19197\right) $ . | 1 |
| 6332 | Find the difference of the vectors $ \vec{v_1} = \left(132163,~20000,~15950\right) $ and $ \vec{v_2} = \left(131372,~20869,~13724\right) $ . | 1 |
| 6333 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~2,~0\right) $ . | 1 |
| 6334 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~0\right) $ and $ \vec{v_2} = \left(3,~2,~-5\right) $ . | 1 |
| 6335 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~-5\right) $ and $ \vec{v_2} = \left(1,~0,~1\right) $ . | 1 |
| 6336 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(-10,~-5,~-8\right) $ . | 1 |
| 6337 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 1 |
| 6338 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~7\right) $ . | 1 |
| 6339 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-5\right) $ . | 1 |
| 6340 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~3\right) $ . | 1 |
| 6341 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~0\right) $ and $ \vec{v_2} = \left(1,~8\right) $ . | 1 |
| 6342 | Find the angle between vectors $ \left(4,~0\right)$ and $\left(1,~8\right)$. | 1 |
| 6343 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(4,~1\right)$. | 1 |
| 6344 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-1\right) $ . | 1 |
| 6345 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~1,~-1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 6346 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~1\right) $ . | 1 |
| 6347 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 4769 }{ 10000 },~0,~\dfrac{ 4769 }{ 10000 }\right) $ . | 1 |
| 6348 | Find the angle between vectors $ \left(-1,~2\right)$ and $\left(5,~2\right)$. | 1 |
| 6349 | Find the angle between vectors $ \left(20,~0\right)$ and $\left(\dfrac{ 293687 }{ 10000 },~\dfrac{ 2113 }{ 500 }\right)$. | 1 |
| 6350 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2,~3\right) $ and $ \vec{v_2} = \left(0,~4,~4\right) $ . | 1 |
