Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3351 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~12\right) $ . | 1 |
| 3352 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ . | 1 |
| 3353 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ . | 1 |
| 3354 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\sqrt{ 3 },~5\right) $ and $ \vec{v_2} = \left(4,~-\sqrt{ 3 },~10\right) $ . | 1 |
| 3355 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\sqrt{ 3 },~5\right) $ and $ \vec{v_2} = \left(4,~-\sqrt{ 3 },~10\right) $ . | 1 |
| 3356 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ . | 1 |
| 3357 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\sqrt{ 3 },~5\right) $ and $ \vec{v_2} = \left(4,~-\sqrt{ 3 },~10\right) $ . | 1 |
| 3358 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~60\right) $ . | 1 |
| 3359 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 9 }{ 41 },~\dfrac{ 40 }{ 41 }\right) $ . | 1 |
| 3360 | Find the difference of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(1,~-4\right) $ . | 1 |
| 3361 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(1,~-4\right)$. | 1 |
| 3362 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(3,~28\right) $ . | 1 |
| 3363 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 9 }{ 41 },~\dfrac{ 40 }{ 41 }\right) $ . | 1 |
| 3364 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(3,~24\right) $ . | 1 |
| 3365 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 4 }{ 9 },~-\dfrac{ 16 }{ 9 }\right) $ and $ \vec{v_2} = \left(36,~100\right) $ . | 1 |
| 3366 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 40 }{ 13 },~-\dfrac{ 96 }{ 13 }\right) $ . | 1 |
| 3367 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~24\right) $ . | 1 |
| 3368 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-7\right) $ . | 1 |
| 3369 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 5 }{ 13 },~\dfrac{ 12 }{ 13 }\right) $ . | 1 |
| 3370 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~5\right) $ and $ \vec{v_2} = \left(6,~-7,~4\right) $ . | 1 |
| 3371 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0,~2\right) $ and $ \vec{v_2} = \left(3,~-1,~1\right) $ . | 1 |
| 3372 | Find the difference of the vectors $ \vec{v_1} = \left(1,~0,~2\right) $ and $ \vec{v_2} = \left(3,~-1,~1\right) $ . | 1 |
| 3373 | Find the sum of the vectors $ \vec{v_1} = \left(0,~1,~-2\right) $ and $ \vec{v_2} = \left(1,~-4,~-2\right) $ . | 1 |
| 3374 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3,~-4\right) $ . | 1 |
| 3375 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~0,~-3\right) $ and $ \vec{v_2} = \left(-1,~-7,~1\right) $ . | 1 |
| 3376 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-7\right) $ . | 1 |
| 3377 | 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 |
| 3378 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~1,~-2\right) $ and $ \vec{v_2} = \left(1,~-1,~-1\right) $ . | 1 |
| 3379 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~-7\right) $ . | 1 |
| 3380 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~8\right) $ . | 1 |
| 3381 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~6\right) $ . | 1 |
| 3382 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 153209 }{ 100000 },~\dfrac{ 64279 }{ 50000 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 120363 }{ 50000 },~\dfrac{ 159727 }{ 50000 }\right) $ . | 1 |
| 3383 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 5 }{ 2 },~3,~-2\right) $ and $ \vec{v_2} = \left(5,~6,~-4\right) $ . | 1 |
| 3384 | Find the angle between vectors $ \left(-1,~2,~-3\right)$ and $\left(4,~-2,~6\right)$. | 1 |
| 3385 | Find the projection of the vector $ \vec{v_1} = \left(1,~6\right) $ on the vector $ \vec{v_2} = \left(-6,~-4\right) $. | 1 |
| 3386 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-126.754,~17.8142\right) $ . | 1 |
| 3387 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~6\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ . | 1 |
| 3388 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~5\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 1 |
| 3389 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~-2\right) $ and $ \vec{v_2} = \left(2,~1,~1\right) $ . | 1 |
| 3390 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-2\right) $ . | 1 |
| 3391 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~20\right) $ . | 1 |
| 3392 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~0\right) $ . | 1 |
| 3393 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~0,~-2\right) $ and $ \vec{v_2} = \left(3,~0,~-2\right) $ . | 1 |
| 3394 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-6\right) $ and $ \vec{v_2} = \left(-7,~5\right) $ . | 1 |
| 3395 | Find the angle between vectors $ \left(-4,~-6\right)$ and $\left(-7,~5\right)$. | 1 |
| 3396 | Find the sum of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(-7,~-14\right) $ . | 1 |
| 3397 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-31647,~3128,~2035\right) $ and $ \vec{v_2} = \left(-\dfrac{ 7 }{ 20 },~-\dfrac{ 63 }{ 25 },~-\dfrac{ 9 }{ 50 }\right) $ . | 1 |
| 3398 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-30044,~3140,~2180\right) $ and $ \vec{v_2} = \left(-\dfrac{ 37 }{ 100 },~-\dfrac{ 129 }{ 50 },~-\dfrac{ 17 }{ 100 }\right) $ . | 1 |
| 3399 | Find the sum of the vectors $ \vec{v_1} = \left(1,~5\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 1 |
| 3400 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~1\right) $ . | 1 |
