Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 251 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-15,~5\right) $ . | 3 |
| 252 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(8,~26\right) $ . | 3 |
| 253 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~14\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 3 |
| 254 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ . | 3 |
| 255 | Find the sum of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 3 |
| 256 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{\sqrt{ 3 }}{ 2 },~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(- \dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right) $ . | 3 |
| 257 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2\right) $ . | 3 |
| 258 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 3 |
| 259 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~0\right) $ and $ \vec{v_2} = \left(5,~8\right) $ . | 3 |
| 260 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ . | 3 |
| 261 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~2\right) $ . | 3 |
| 262 | Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(-8,~5\right) $ . | 3 |
| 263 | Find the angle between vectors $ \left(9,~2\right)$ and $\left(3,~1\right)$. | 3 |
| 264 | Find the angle between vectors $ \left(9,~8\right)$ and $\left(2,~0\right)$. | 3 |
| 265 | Find the difference of the vectors $ \vec{v_1} = \left(3,~11\right) $ and $ \vec{v_2} = \left(-4,~10\right) $ . | 3 |
| 266 | Find the sum of the vectors $ \vec{v_1} = \left(-24,~4\right) $ and $ \vec{v_2} = \left(13,~14\right) $ . | 3 |
| 267 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-2\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 3 |
| 268 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 3 |
| 269 | Determine whether the vectors $ \vec{v_1} = \left(-7,~7\right) $ and $ \vec{v_2} = \left(1,~22\right) $ are linearly independent or dependent. | 3 |
| 270 | Find the angle between vectors $ \left(-5,~2\right)$ and $\left(10,~4\right)$. | 3 |
| 271 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 3 |
| 272 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~5\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 3 |
| 273 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 3 |
| 274 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ . | 3 |
| 275 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(\dfrac{ 34641 }{ 20000 },~3\right) $ . | 3 |
| 276 | Find the angle between vectors $ \left(5,~6\right)$ and $\left(4,~2\right)$. | 3 |
| 277 | Find the difference of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(6,~5\right) $ . | 3 |
| 278 | Find the projection of the vector $ \vec{v_1} = \left(5,~-5,~2\right) $ on the vector $ \vec{v_2} = \left(1,~1,~5\right) $. | 3 |
| 279 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-4\right) $ . | 3 |
| 280 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-2\right) $ . | 3 |
| 281 | Find the angle between vectors $ \left(3,~7\right)$ and $\left(-4,~-1\right)$. | 3 |
| 282 | Find the angle between vectors $ \left(9,~-7\right)$ and $\left(8,~3\right)$. | 3 |
| 283 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 3 |
| 284 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-7\right) $ and $ \vec{v_2} = \left(-13,~12\right) $ . | 3 |
| 285 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 3 |
| 286 | Determine whether the vectors $ \vec{v_1} = \left(-\sqrt{ 160 },~\sqrt{ 40 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 6 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ are linearly independent or dependent. | 3 |
| 287 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-6\right) $ and $ \vec{v_2} = \left(-15,~8\right) $ . | 3 |
| 288 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(-4,~-6\right) $ . | 3 |
| 289 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 3 |
| 290 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~7\right) $ . | 3 |
| 291 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-1\right) $ . | 3 |
| 292 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~5\right) $ . | 3 |
| 293 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~7,~-9\right) $ and $ \vec{v_2} = \left(-11,~9,~-2\right) $ . | 3 |
| 294 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-3\right) $ . | 3 |
| 295 | Find the angle between vectors $ \left(3,~-2\right)$ and $\left(5,~1\right)$. | 3 |
| 296 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 173 }{ 10 },~10\right) $ and $ \vec{v_2} = \left(-\dfrac{ 63 }{ 10 },~\dfrac{ 68 }{ 5 }\right) $ . | 3 |
| 297 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 3 |
| 298 | Find the sum of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(10,~-120\right) $ . | 3 |
| 299 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-4,~-12\right) $ . | 3 |
| 300 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~8\right) $ . | 3 |
