Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3301 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 1531 }{ 5 },~\dfrac{ 71 }{ 5 },~-\dfrac{ 621 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1827 }{ 10 },~\dfrac{ 99 }{ 5 },~-\dfrac{ 752 }{ 5 }\right) $ . | 1 |
| 3302 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~170\right) $ . | 1 |
| 3303 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~5\right) $ . | 1 |
| 3304 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 1 |
| 3305 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ . | 1 |
| 3306 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-1,~-1\right) $ . | 1 |
| 3307 | Determine whether the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(-9,~-2\right) $ are linearly independent or dependent. | 1 |
| 3308 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~3\right) $ . | 1 |
| 3309 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~2 \sqrt{ 3 }\right) $ . | 1 |
| 3310 | Find the angle between vectors $ \left(2,~2,~-3\right)$ and $\left(1,~-2,~-2\right)$. | 1 |
| 3311 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4,~12\right) $ and $ \vec{v_2} = \left(2,~-2,~4\right) $ . | 1 |
| 3312 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(4,~-8\right) $ . | 1 |
| 3313 | Find the angle between vectors $ \left(2,~1,~1\right)$ and $\left(4,~-1,~0\right)$. | 1 |
| 3314 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 3315 | Find the angle between vectors $ \left(2,~-3,~4\right)$ and $\left(-1,~\dfrac{ 3 }{ 2 },~-2\right)$. | 1 |
| 3316 | Find the angle between vectors $ \left(5,~-4,~-3\right)$ and $\left(2,~1,~2\right)$. | 1 |
| 3317 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8.4,~14.7\right) $ . | 1 |
| 3318 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 2 },~0,~0\right) $ and $ \vec{v_2} = \left(\sqrt{ 3 },~2 \sqrt{ 3 },~1\right) $ . | 1 |
| 3319 | Find the angle between vectors $ \left(\dfrac{ 3 }{ 2 },~0,~0\right)$ and $\left(\sqrt{ 3 },~2 \sqrt{ 3 },~1\right)$. | 1 |
| 3320 | Find the angle between vectors $ \left(\dfrac{ 3 }{ 2 },~0,~\dfrac{\sqrt{ 3 }}{ 2 }\right)$ and $\left(\sqrt{ 3 },~2 \sqrt{ 3 },~1\right)$. | 1 |
| 3321 | Find the angle between vectors $ \left(5,~-5\right)$ and $\left(-10,~10\right)$. | 1 |
| 3322 | Find the projection of the vector $ \vec{v_1} = \left(-2,~7,~-3\right) $ on the vector $ \vec{v_2} = \left(-1,~3,~1\right) $. | 1 |
| 3323 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~2,~-4\right) $ and $ \vec{v_2} = \left(1,~1,~-6\right) $ . | 1 |
| 3324 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 1 |
| 3325 | Find the sum of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
| 3326 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-4,~4\right) $ and $ \vec{v_2} = \left(0,~2,~-1\right) $ . | 1 |
| 3327 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-4,~4\right) $ . | 1 |
| 3328 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-4,~4\right) $ and $ \vec{v_2} = \left(0,~2,~-1\right) $ . | 1 |
| 3329 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-6,~5\right) $ . | 1 |
| 3330 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~12\right) $ . | 1 |
| 3331 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~12\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 1 |
| 3332 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(-2,~6\right) $ . | 1 |
| 3333 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(-2,~-6\right) $ . | 1 |
| 3334 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-5\right) $ and $ \vec{v_2} = \left(-9,~1\right) $ . | 1 |
| 3335 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~9\right) $ and $ \vec{v_2} = \left(9,~9\right) $ . | 1 |
| 3336 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~18\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ . | 1 |
| 3337 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(-12,~2\right) $ . | 1 |
| 3338 | Find the projection of the vector $ \vec{v_1} = \left(4,~-5,~3\right) $ on the vector $ \vec{v_2} = \left(-2,~5,~5\right) $. | 1 |
| 3339 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~3,~10\right) $ . | 1 |
| 3340 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~1,~2\right) $ and $ \vec{v_2} = \left(-4,~-2,~0\right) $ . | 1 |
| 3341 | Determine whether the vectors $ \vec{v_1} = \left(3,~3,~10\right) $, $ \vec{v_2} = \left(7,~5,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 3342 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~10\right) $ and $ \vec{v_2} = \left(7,~5,~0\right) $ . | 1 |
| 3343 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 7 },~\dfrac{ 5 }{ 7 }\right) $ and $ \vec{v_2} = \left(8,~27\right) $ . | 1 |
| 3344 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ and $ \vec{v_2} = \left(4,~28\right) $ . | 1 |
| 3345 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 19 }{ 5 },~\dfrac{ 142 }{ 5 }\right) $ . | 1 |
| 3346 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
| 3347 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~15\right) $ . | 1 |
| 3348 | Find the projection of the vector $ \vec{v_1} = \left(1,~-6\right) $ on the vector $ \vec{v_2} = \left(2,~-1\right) $. | 1 |
| 3349 | 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 |
| 3350 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 8 }{ 17 },~\dfrac{ 15 }{ 17 }\right) $ . | 1 |
