Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3401 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
| 3402 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 1 |
| 3403 | Find the sum of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(-10,~7\right) $ . | 1 |
| 3404 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
| 3405 | Find the projection of the vector $ \vec{v_1} = \left(1,~3,~1\right) $ on the vector $ \vec{v_2} = \left(-1,~1,~-2\right) $. | 1 |
| 3406 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ . | 1 |
| 3407 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9,~-1,~3\right) $ and $ \vec{v_2} = \left(-3,~0,~1\right) $ . | 1 |
| 3408 | Find the angle between vectors $ \left(-1,~6,~1\right)$ and $\left(1,~-5,~0\right)$. | 1 |
| 3409 | Find the angle between vectors $ \left(3,~6\right)$ and $\left(\sqrt{ 2 },~-\dfrac{ 1 }{ 3 }\right)$. | 1 |
| 3410 | Find the angle between vectors $ \left(4,~3,~3\right)$ and $\left(3,~2,~0\right)$. | 1 |
| 3411 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 131387671 }{ 100000 },~7.9,~-\dfrac{ 27292229 }{ 20000 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 147318127 }{ 100000 },~11.2657,~-695.7339\right) $ . | 1 |
| 3412 | Find the angle between vectors $ \left(50,~105\right)$ and $\left(64,~130\right)$. | 1 |
| 3413 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~7\right) $ and $ \vec{v_2} = \left(0,~-21\right) $ . | 1 |
| 3414 | Find the sum of the vectors $ \vec{v_1} = \left(7,~4,~-3\right) $ and $ \vec{v_2} = \left(2,~1,~5\right) $ . | 1 |
| 3415 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(-2,~-5\right) $ . | 1 |
| 3416 | Find the angle between vectors $ \left(1,~9\right)$ and $\left(-3,~5\right)$. | 1 |
| 3417 | Find the angle between vectors $ \left(-1,~-2\right)$ and $\left(4,~2\right)$. | 1 |
| 3418 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(-2,~-5\right) $ . | 1 |
| 3419 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-5\right) $ and $ \vec{v_2} = \left(-8,~7\right) $ . | 1 |
| 3420 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(-8,~7\right) $ . | 1 |
| 3421 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~2\right) $ . | 1 |
| 3422 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~3,~-1\right) $ and $ \vec{v_2} = \left(1,~-1,~-1\right) $ . | 1 |
| 3423 | Find the projection of the vector $ \vec{v_1} = \left(2,~4\right) $ on the vector $ \vec{v_2} = \left(-1,~7\right) $. | 1 |
| 3424 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~-2\right) $ and $ \vec{v_2} = \left(0,~3,~-6\right) $ . | 1 |
| 3425 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~4,~2\right) $ and $ \vec{v_2} = \left(0,~1,~-6\right) $ . | 1 |
| 3426 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{\sqrt{ 3 }}{ 2 },~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(\sqrt{ 3 },~1\right) $ . | 1 |
| 3427 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{\sqrt{ 3 }}{ 2 },~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(-\sqrt{ 3 },~1\right) $ . | 1 |
| 3428 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~-1,~2\right) $ . | 1 |
| 3429 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~5,~-8\right) $ and $ \vec{v_2} = \left(2,~7,~0\right) $ . | 1 |
| 3430 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(-4,~7,~-6\right) $ . | 1 |
| 3431 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~-3\right) $ and $ \vec{v_2} = \left(1,~4,~5\right) $ . | 1 |
| 3432 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~-3\right) $ . | 1 |
| 3433 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~3,~1\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 3434 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 113701 }{ 10000 },~\dfrac{ 630253 }{ 100000 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 51 }{ 5 },~-\dfrac{ 68 }{ 5 }\right) $ . | 1 |
| 3435 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 113701 }{ 10000 },~\dfrac{ 630253 }{ 100000 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 51 }{ 5 },~-\dfrac{ 68 }{ 5 },~0\right) $ . | 1 |
| 3436 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-1,~1\right) $ . | 1 |
| 3437 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
| 3438 | Find the angle between vectors $ \left(1,~0,~2\right)$ and $\left(2,~-1,~1\right)$. | 1 |
| 3439 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~6,~8\right) $ . | 1 |
| 3440 | Find the angle between vectors $ \left(2,~4,~-1\right)$ and $\left(-3,~0,~6\right)$. | 1 |
| 3441 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~5,~9\right) $ and $ \vec{v_2} = \left(2,~5,~4\right) $ . | 1 |
| 3442 | Find the projection of the vector $ \vec{v_1} = \left(-9,~9,~9\right) $ on the vector $ \vec{v_2} = \left(6,~7,~6\right) $. | 1 |
| 3443 | Find the projection of the vector $ \vec{v_1} = \left(6,~7,~6\right) $ on the vector $ \vec{v_2} = \left(-9,~9,~9\right) $. | 1 |
| 3444 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-3\right) $ . | 1 |
| 3445 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 1 |
| 3446 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~7\right) $ . | 1 |
| 3447 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~3\right) $ . | 1 |
| 3448 | Find the difference of the vectors $ \vec{v_1} = \left(0,~3\right) $ and $ \vec{v_2} = \left(3,~7\right) $ . | 1 |
| 3449 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-5\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ . | 1 |
| 3450 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 53 }{ 250 },~-\dfrac{ 989 }{ 1000 },~-\dfrac{ 347 }{ 1000 }\right) $ . | 1 |
