Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1351 | Find the angle between vectors $ \left(2,~3\right)$ and $\left(-1,~-2\right)$. | 2 |
1352 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right)$ and $\left(\dfrac{ 683 }{ 1000 },~-\dfrac{ 683 }{ 1000 }\right)$. | 2 |
1353 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-5\right) $ and $ \vec{v_2} = \left(2,~-8\right) $ . | 2 |
1354 | Find the angle between vectors $ \left(-\dfrac{ 131 }{ 200 },~-\dfrac{ 29 }{ 200 }\right)$ and $\left(\dfrac{ 77 }{ 1000 },~-\dfrac{ 409 }{ 1000 }\right)$. | 2 |
1355 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~1\right) $ and $ \vec{v_2} = \left(2,~-4\right) $ . | 2 |
1356 | Find the magnitude of the vector $ \| \vec{v} \| = \left(18,~8\right) $ . | 2 |
1357 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-4\right) $ . | 2 |
1358 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 2 |
1359 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 683 }{ 1000 },~-\dfrac{ 683 }{ 1000 }\right) $. | 2 |
1360 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~7\right) $ and $ \vec{v_2} = \left(1,~22\right) $ . | 2 |
1361 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-6\right) $ . | 2 |
1362 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~2\right) $ and $ \vec{v_2} = \left(2,~4,~2\right) $ . | 2 |
1363 | Calculate the dot product of the vectors $ \vec{v_1} = \left(15,~15\right) $ and $ \vec{v_2} = \left(-5,~4\right) $ . | 2 |
1364 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
1365 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~6\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ . | 2 |
1366 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 2 |
1367 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~6\right) $ . | 2 |
1368 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-4,~6\right) $ . | 2 |
1369 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 2 |
1370 | Find the difference of the vectors $ \vec{v_1} = \left(3,~7\right) $ and $ \vec{v_2} = \left(9,~2\right) $ . | 2 |
1371 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~4\right) $ and $ \vec{v_2} = \left(-7,~1\right) $ . | 2 |
1372 | Find the angle between vectors $ \left(-2,~-3\right)$ and $\left(6,~-1\right)$. | 2 |
1373 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-18,~14\right) $ . | 2 |
1374 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~-5\right) $ and $ \vec{v_2} = \left(7,~10\right) $ . | 2 |
1375 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 2 |
1376 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0.1111,~0.8889\right) $ . | 2 |
1377 | Find the difference of the vectors $ \vec{v_1} = \left(330,~0\right) $ and $ \vec{v_2} = \left(200,~-120\right) $ . | 2 |
1378 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(-2,~5\right)$. | 2 |
1379 | Find the angle between vectors $ \left(\dfrac{ 7 }{ 5 },~\dfrac{ 121 }{ 50 }\right)$ and $\left(\dfrac{ 19 }{ 20 },~\dfrac{ 33 }{ 20 }\right)$. | 2 |
1380 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 41 }{ 10 },~\dfrac{ 9 }{ 10 }\right) $ . | 2 |
1381 | Find the angle between vectors $ \left(1,~1\right)$ and $\left(1,~-1\right)$. | 2 |
1382 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~12\right) $ and $ \vec{v_2} = \left(6,~9\right) $ . | 2 |
1383 | Find the difference of the vectors $ \vec{v_1} = \left(12,~-4\right) $ and $ \vec{v_2} = \left(32,~24\right) $ . | 2 |
1384 | Find the projection of the vector $ \vec{v_1} = \left(-3,~1,~5\right) $ on the vector $ \vec{v_2} = \left(-2,~3,~8\right) $. | 2 |
1385 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~4\right) $ . | 2 |
1386 | Find the difference of the vectors $ \vec{v_1} = \left(13,~7\right) $ and $ \vec{v_2} = \left(9,~2\right) $ . | 2 |
1387 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1\right) $ . | 2 |
1388 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~-4\right) $ and $ \vec{v_2} = \left(-10,~-10,~20\right) $ . | 2 |
1389 | Find the projection of the vector $ \vec{v_1} = \left(3,~3\right) $ on the vector $ \vec{v_2} = \left(5,~1\right) $. | 2 |
1390 | Find the angle between vectors $ \left(0,~5\right)$ and $\left(-6,~1\right)$. | 2 |
1391 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-8,~6\right) $ . | 2 |
1392 | Find the projection of the vector $ \vec{v_1} = \left(-3,~4,~-\sqrt{ 7 }\right) $ on the vector $ \vec{v_2} = \left(3,~-4,~\sqrt{ 7 }\right) $. | 2 |
1393 | Find the angle between vectors $ \left(3,~1,~2\right)$ and $\left(2,~4,~2\right)$. | 2 |
1394 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(4.1623,~2.1623\right)$. | 2 |
1395 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(4,~4\right) $ . | 2 |
1396 | Find the projection of the vector $ \vec{v_1} = \left(3,~6\right) $ on the vector $ \vec{v_2} = \left(8,~-4\right) $. | 2 |
1397 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4\right) $ . | 2 |
1398 | Find the angle between vectors $ \left(18,~12\right)$ and $\left(6,~4\right)$. | 2 |
1399 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2,~-3\right) $ . | 2 |
1400 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~6\right) $ . | 2 |