Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6401 | Calculate the cross product of the vectors $ \vec{v_1} = \left(93,~128,~92\right) $ and $ \vec{v_2} = \left(4,~-2,~3\right) $ . | 1 |
6402 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~3\right) $ . | 1 |
6403 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~-3,~-2\right) $ . | 1 |
6404 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~1\right) $ . | 1 |
6405 | Find the sum of the vectors $ \vec{v_1} = \left(-18,~6\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 1 |
6406 | Find the angle between vectors $ \left(-7,~4\right)$ and $\left(5,~\dfrac{ 35 }{ 4 }\right)$. | 1 |
6407 | 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 |
6408 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(2,~4,~-1\right) $ . | 1 |
6409 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~0\right) $ and $ \vec{v_2} = \left(0,~3,~-5\right) $ . | 1 |
6410 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 657 }{ 1000 },~\dfrac{ 13 }{ 500 },~\dfrac{ 377 }{ 500 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 293 }{ 500 },~-\dfrac{ 807 }{ 1000 },~\dfrac{ 69 }{ 1000 }\right) $ . | 1 |
6411 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-2,~5\right) $ and $ \vec{v_2} = \left(2,~1,~4\right) $ . | 1 |
6412 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(-5,~5,~0\right) $ . | 1 |
6413 | Find the angle between vectors $ \left(-3,~-9\right)$ and $\left(2,~-4\right)$. | 1 |
6414 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $ and $ \vec{v_2} = \left(4,~-5,~6\right) $ . | 1 |
6415 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~0\right) $ and $ \vec{v_2} = \left(1,~1,~-1\right) $ . | 1 |
6416 | Find the sum of the vectors $ \vec{v_1} = \left(8,~-4\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 1 |
6417 | Find the angle between vectors $ \left(3,~3\right)$ and $\left(4,~4\right)$. | 1 |
6418 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-2,~2\right) $ and $ \vec{v_2} = \left(5,~5,~-5\right) $ . | 1 |
6419 | Determine whether the vectors $ \vec{v_1} = \left(6,~-23\right) $ and $ \vec{v_2} = \left(46,~-12\right) $ are linearly independent or dependent. | 1 |
6420 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-3 \sqrt{ 3 }\right) $ . | 1 |
6421 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ . | 1 |
6422 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-4,~-3\right) $ and $ \vec{v_2} = \left(-4,~-3,~-2\right) $ . | 1 |
6423 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
6424 | Find the projection of the vector $ \vec{v_1} = \left(0,~1,~\sqrt{ 3 }\right) $ on the vector $ \vec{v_2} = \left(-1,~\sqrt{ 3 },~-1\right) $. | 1 |
6425 | Find the sum of the vectors $ \vec{v_1} = \left(18,~-6\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 1 |
6426 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~5,~5\right) $ . | 1 |
6427 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-10,~11\right) $ and $ \vec{v_2} = \left(3,~0,~-4\right) $ . | 1 |
6428 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(-2,~-14,~9\right) $ . | 1 |
6429 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(1,~-2\right) $ are linearly independent or dependent. | 1 |
6430 | Find the difference of the vectors $ \vec{v_1} = \left(-107253,~83672,~4181\right) $ and $ \vec{v_2} = \left(-112571,~84706,~4980\right) $ . | 1 |
6431 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~4\right) $ . | 1 |
6432 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(-5,~5,~0\right) $ . | 1 |
6433 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-9,~6,~-6\right) $ and $ \vec{v_2} = \left(3,~-2,~2\right) $ . | 1 |
6434 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~9,~6\right) $ and $ \vec{v_2} = \left(-8,~3,~-2\right) $ . | 1 |
6435 | 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 |
6436 | Determine whether the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(4,~-3,~4\right)$ are linearly independent or dependent. | 1 |
6437 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~-7\right) $ and $ \vec{v_2} = \left(8,~2\right) $ . | 1 |
6438 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~5,~2\right) $ and $ \vec{v_2} = \left(6,~3,~1\right) $ . | 1 |
6439 | Calculate the cross product of the vectors $ \vec{v_1} = \left(30,~0,~0\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
6440 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 19 }{ 5 },~\dfrac{ 142 }{ 5 }\right) $ . | 1 |
6441 | Calculate the cross product of the vectors $ \vec{v_1} = \left(33,~-24,~-30\right) $ and $ \vec{v_2} = \left(-11,~8,~10\right) $ . | 1 |
6442 | Find the angle between vectors $ \left(16,~4,~-2\right)$ and $\left(8,~2,~-1\right)$. | 1 |
6443 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 10 }\right) $ . | 1 |
6444 | Find the sum of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
6445 | Determine whether the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(-2,~6\right) $ are linearly independent or dependent. | 1 |
6446 | Find the sum of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ . | 1 |
6447 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~-1,~0\right) $ . | 1 |
6448 | Find the difference of the vectors $ \vec{v_1} = \left(0,~8,~4\right) $ and $ \vec{v_2} = \left(5,~8,~5\right) $ . | 1 |
6449 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1,~1\right) $ and $ \vec{v_2} = \left(-2,~2,~3\right) $ . | 1 |
6450 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~-3\right) $ and $ \vec{v_2} = \left(-2,~0,~-5\right) $ . | 1 |