Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4351 | Find the angle between vectors $ \left(-3,~2,~-5\right)$ and $\left(1,~1,~4\right)$. | 1 |
| 4352 | Find the angle between vectors $ \left(6,~0\right)$ and $\left(8,~0\right)$. | 1 |
| 4353 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~1\right) $ . | 1 |
| 4354 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~1\right) $ and $ \vec{v_2} = \left(3,~-7\right) $ . | 1 |
| 4355 | Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(2,~0\right) $. | 1 |
| 4356 | Find the angle between vectors $ \left(-\dfrac{ 1299 }{ 100 },~\dfrac{ 15 }{ 2 }\right)$ and $\left(\dfrac{ 909 }{ 50 },~\dfrac{ 21 }{ 2 }\right)$. | 1 |
| 4357 | Find the angle between vectors $ \left(-2,~6\right)$ and $\left(-6,~12\right)$. | 1 |
| 4358 | Find the angle between vectors $ \left(-2,~6\right)$ and $\left(6,~-2\right)$. | 1 |
| 4359 | Find the angle between vectors $ \left(-2,~6\right)$ and $\left(-1,~3\right)$. | 1 |
| 4360 | Find the angle between vectors $ \left(5,~6\right)$ and $\left(7,~1\right)$. | 1 |
| 4361 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 5645117 }{ 100 },~-\dfrac{ 770859 }{ 50 },~\dfrac{ 429504 }{ 25 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 5643497 }{ 100 },~-\dfrac{ 1541283 }{ 100 },~\dfrac{ 858759 }{ 50 }\right) $ . | 1 |
| 4362 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 5645117 }{ 100 },~-\dfrac{ 770859 }{ 50 },~\dfrac{ 429504 }{ 25 }\right) $ . | 1 |
| 4363 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 5645117 }{ 100 },~-\dfrac{ 770859 }{ 50 },~\dfrac{ 429504 }{ 25 }\right) $, $ \vec{v_2} = \left(\dfrac{ 5643497 }{ 100 },~-\dfrac{ 1541283 }{ 100 },~\dfrac{ 858759 }{ 50 }\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 4364 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 5645117 }{ 100 },~-\dfrac{ 770859 }{ 50 },~\dfrac{ 429504 }{ 25 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 5643497 }{ 100 },~-\dfrac{ 1541283 }{ 100 },~\dfrac{ 858759 }{ 50 }\right) $. | 1 |
| 4365 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-1\right) $ . | 1 |
| 4366 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~8\right) $ . | 1 |
| 4367 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 683 }{ 1000 },~-\dfrac{ 683 }{ 1000 }\right) $ . | 1 |
| 4368 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-4\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ . | 1 |
| 4369 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ . | 1 |
| 4370 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(-2,~3,~5\right) $ . | 1 |
| 4371 | Find the sum of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ . | 1 |
| 4372 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-3\right) $ . | 1 |
| 4373 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-14,~5\right) $ . | 1 |
| 4374 | Find the sum of the vectors $ \vec{v_1} = \left(3,~12\right) $ and $ \vec{v_2} = \left(0,~6\right) $ . | 1 |
| 4375 | Find the difference of the vectors $ \vec{v_1} = \left(3,~12\right) $ and $ \vec{v_2} = \left(0,~6\right) $ . | 1 |
| 4376 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~12\right) $ . | 1 |
| 4377 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~0,~1\right) $ . | 1 |
| 4378 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4,~-2\right) $ . | 1 |
| 4379 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 2 },~\dfrac{ 49 }{ 10 },~30\right) $ . | 1 |
| 4380 | Find the difference of the vectors $ \vec{v_1} = \left(6,~9,~-18\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
| 4381 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4,~-\sqrt{ 7 }\right) $ and $ \vec{v_2} = \left(3,~-4,~\sqrt{ 7 }\right) $ . | 1 |
| 4382 | Find the angle between vectors $ \left(-3,~4,~-\sqrt{ 7 }\right)$ and $\left(3,~-4,~\sqrt{ 7 }\right)$. | 1 |
| 4383 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~4,~-\sqrt{ 7 }\right) $ . | 1 |
| 4384 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-2,~-4\right) $ and $ \vec{v_2} = \left(4,~-4,~0\right) $ . | 1 |
| 4385 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~11\right) $ . | 1 |
| 4386 | Find the projection of the vector $ \vec{v_1} = \left(11,~11\right) $ on the vector $ \vec{v_2} = \left(9,~-4\right) $. | 1 |
| 4387 | Find the angle between vectors $ \left(5,~3\right)$ and $\left(4,~-8\right)$. | 1 |
| 4388 | Find the difference of the vectors $ \vec{v_1} = \left(7,~5\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 4389 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 259 }{ 100 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(0,~3\right) $ . | 1 |
| 4390 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 259 }{ 100 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(0,~3\right) $ . | 1 |
| 4391 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~-2\right) $ and $ \vec{v_2} = \left(2,~0,~3\right) $ . | 1 |
| 4392 | Determine whether the vectors $ \vec{v_1} = \left(4,~4\right) $ and $ \vec{v_2} = \left(0,~0\right) $ are linearly independent or dependent. | 1 |
| 4393 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~1,~2\right) $ and $ \vec{v_2} = \left(3,~-2,~4\right) $ . | 1 |
| 4394 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~14,~1\right) $ and $ \vec{v_2} = \left(4,~4,~2\right) $ . | 1 |
| 4395 | Find the projection of the vector $ \vec{v_1} = \left(4,~5\right) $ on the vector $ \vec{v_2} = \left(6,~8\right) $. | 1 |
| 4396 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 1 |
| 4397 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-9,~10\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 4398 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-9,~10\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 4399 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3,~-2\right) $ and $ \vec{v_2} = \left(-2,~-9,~9\right) $ . | 1 |
| 4400 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-3\right) $ . | 1 |
