Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1401 | Find the projection of the vector $ \vec{v_1} = \left(3,~-4,~\sqrt{ 7 }\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $. | 2 |
1402 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3,~2\right) $ . | 2 |
1403 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 2 |
1404 | Find the sum of the vectors $ \vec{v_1} = \left(9,~4\right) $ and $ \vec{v_2} = \left(1,~7\right) $ . | 2 |
1405 | Find the angle between vectors $ \left(1,~5,~-1\right)$ and $\left(5,~-1,~1\right)$. | 2 |
1406 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(-\dfrac{ 9 }{ 2 },~0\right) $ . | 2 |
1407 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 183 }{ 1000 },~-\dfrac{ 183 }{ 1000 }\right) $ and $ \vec{v_2} = \left(- \dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right) $ . | 2 |
1408 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-4,~\sqrt{ 7 }\right) $ . | 2 |
1409 | Find the angle between vectors $ \left(1,~5,~-1\right)$ and $\left(-1,~1,~4\right)$. | 2 |
1410 | Find the sum of the vectors $ \vec{v_1} = \left(-9,~9\right) $ and $ \vec{v_2} = \left(-4,~-5\right) $ . | 2 |
1411 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 2 |
1412 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 2 },~0\right) $ . | 2 |
1413 | Find the projection of the vector $ \vec{v_1} = \left(3,~-5\right) $ on the vector $ \vec{v_2} = \left(-4,~6\right) $. | 2 |
1414 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 2 |
1415 | Find the angle between vectors $ \left(2,~-2,~2\right)$ and $\left(1,~1,~1\right)$. | 2 |
1416 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 2 |
1417 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~4\right) $ . | 2 |
1418 | Find the angle between vectors $ \left(4,~-5\right)$ and $\left(3,~7\right)$. | 2 |
1419 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(-4,~6\right) $ . | 2 |
1420 | Find the angle between vectors $ \left(1,~5,~-1\right)$ and $\left(-1,~-1,~5\right)$. | 2 |
1421 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-\dfrac{ 3 }{ 100 },~\dfrac{ 99 }{ 100 }\right) $ and $ \vec{v_2} = \left(0,~-1,~0\right) $ . | 2 |
1422 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 2 },~0\right) $ . | 2 |
1423 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-12\right) $ . | 2 |
1424 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-4\right) $ and $ \vec{v_2} = \left(1,~-9\right) $ . | 2 |
1425 | Find the projection of the vector $ \vec{v_1} = \left(3,~-4\right) $ on the vector $ \vec{v_2} = \left(-18,~24\right) $. | 2 |
1426 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-46,~-42\right) $ . | 2 |
1427 | Find the difference of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(9,~3\right) $ . | 2 |
1428 | Find the angle between vectors $ \left(-5,~-1,~1\right)$ and $\left(5,~-1,~1\right)$. | 2 |
1429 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 2 |
1430 | Find the projection of the vector $ \vec{v_1} = \left(5,~-3\right) $ on the vector $ \vec{v_2} = \left(13,~8\right) $. | 2 |
1431 | Find the magnitude of the vector $ \| \vec{v} \| = \left(15,~8\right) $ . | 2 |
1432 | 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) $ . | 2 |
1433 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 2 |
1434 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~6\right) $ . | 2 |
1435 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~-5\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 2 |
1436 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(1,~-2\right) $ . | 2 |
1437 | Find the magnitude of the vector $ \| \vec{v} \| = \left(80,~28\right) $ . | 2 |
1438 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-3,~2\right) $ and $ \vec{v_2} = \left(-3,~9,~-6\right) $ . | 2 |
1439 | Find the angle between vectors $ \left(-5,~-1,~1\right)$ and $\left(-1,~1,~4\right)$. | 2 |
1440 | Find the projection of the vector $ \vec{v_1} = \left(-1,~-2\right) $ on the vector $ \vec{v_2} = \left(0,~5\right) $. | 2 |
1441 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 2 |
1442 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-15,~-8\right) $ . | 2 |
1443 | Find the angle between vectors $ \left(-1,~-2\right)$ and $\left(0,~5\right)$. | 2 |
1444 | Calculate the dot product of the vectors $ \vec{v_1} = \left(22,~15\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 2 |
1445 | Find the sum of the vectors $ \vec{v_1} = \left(-9,~4\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 2 |
1446 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 2 |
1447 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 2 |
1448 | Find the angle between vectors $ \left(1,~2,~2\right)$ and $\left(2,~2,~1\right)$. | 2 |
1449 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 2 |
1450 | Find the difference of the vectors $ \vec{v_1} = \left(220,~10\right) $ and $ \vec{v_2} = \left(-190,~295\right) $ . | 2 |