Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1301 | Find the angle between vectors $ \left(1,~3\right)$ and $\left(2,~1\right)$. | 2 |
1302 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(-7,~-14\right) $ . | 2 |
1303 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(-10,~-8\right) $ . | 2 |
1304 | Find the difference of the vectors $ \vec{v_1} = \left(-7,~7\right) $ and $ \vec{v_2} = \left(1,~22\right) $ . | 2 |
1305 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-4\right) $ . | 2 |
1306 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-2\right) $ . | 2 |
1307 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 2 |
1308 | Find the angle between vectors $ \left(-3,~3\right)$ and $\left(9,~-9\right)$. | 2 |
1309 | Find the difference of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 2 |
1310 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~9,~9\right) $ and $ \vec{v_2} = \left(9,~9,~9\right) $ . | 2 |
1311 | Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(0,~-5\right) $ . | 2 |
1312 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~4\right) $ . | 2 |
1313 | Find the angle between vectors $ \left(-3,~5\right)$ and $\left(-7,~-1\right)$. | 2 |
1314 | Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(6,~-9\right) $ . | 2 |
1315 | Determine whether the vectors $ \vec{v_1} = \left(-1,~-2\right) $ and $ \vec{v_2} = \left(8,~-4\right) $ are linearly independent or dependent. | 2 |
1316 | Find the angle between vectors $ \left(-2,~5\right)$ and $\left(6,~2\right)$. | 2 |
1317 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-10,~5\right) $ and $ \vec{v_2} = \left(0,~-1.688,~4.24\right) $ . | 2 |
1318 | Determine whether the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(-1,~-1\right) $ are linearly independent or dependent. | 2 |
1319 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(7,~17\right) $ . | 2 |
1320 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(9,~3\right) $ . | 2 |
1321 | Find the difference of the vectors $ \vec{v_1} = \left(330,~0\right) $ and $ \vec{v_2} = \left(175,~-120\right) $ . | 2 |
1322 | Find the sum of the vectors $ \vec{v_1} = \left(2,~9\right) $ and $ \vec{v_2} = \left(9,~0\right) $ . | 2 |
1323 | Find the sum of the vectors $ \vec{v_1} = \left(0,~6\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 2 |
1324 | Determine whether the vectors $ \vec{v_1} = \left(-6,~2\right) $ and $ \vec{v_2} = \left(-12,~36\right) $ are linearly independent or dependent. | 2 |
1325 | Find the angle between vectors $ \left(\dfrac{ 3 }{ 4 },~2\right)$ and $\left(3,~-2\right)$. | 2 |
1326 | Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 1 }{ 10 },~\dfrac{ 1 }{ 5 }\right) $. | 2 |
1327 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(8,~4\right) $ . | 2 |
1328 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 2 |
1329 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~6\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 2 |
1330 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(16,~12\right) $ . | 2 |
1331 | Find the projection of the vector $ \vec{v_1} = \left(6,~17\right) $ on the vector $ \vec{v_2} = \left(11,~-11\right) $. | 2 |
1332 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~4.5,~2\right) $ and $ \vec{v_2} = \left(0,~2.6,~2.6\right) $ . | 2 |
1333 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-12,~5\right) $ . | 2 |
1334 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~8\right) $ and $ \vec{v_2} = \left(9,~-2\right) $ . | 2 |
1335 | 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{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right) $. | 2 |
1336 | Find the sum of the vectors $ \vec{v_1} = \left(0,~2,~-3\right) $ and $ \vec{v_2} = \left(2,~6,~4\right) $ . | 2 |
1337 | Determine whether the vectors $ \vec{v_1} = \left(6,~17\right) $ and $ \vec{v_2} = \left(11,~-11\right) $ are linearly independent or dependent. | 2 |
1338 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~-2,~2\right) $ . | 2 |
1339 | Find the sum of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(-5,~0\right) $ . | 2 |
1340 | Find the angle between vectors $ \left(-3,~5\right)$ and $\left(-4,~-6\right)$. | 2 |
1341 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(5,~-6\right) $ . | 2 |
1342 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~8\right) $ . | 2 |
1343 | Determine whether the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(-12,~36\right) $ are linearly independent or dependent. | 2 |
1344 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 3 }{ 2 },~\dfrac{ 15 }{ 2 }\right) $ . | 2 |
1345 | Find the angle between vectors $ \left(1,~1\right)$ and $\left(1,~1\right)$. | 2 |
1346 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right)$ and $\left(- \dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right)$. | 2 |
1347 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~2\right) $ and $ \vec{v_2} = \left(0,~1,~-2\right) $ . | 2 |
1348 | Find the sum of the vectors $ \vec{v_1} = \left(0,~-30\right) $ and $ \vec{v_2} = \left(-9,~-27\right) $ . | 2 |
1349 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~7\right) $ and $ \vec{v_2} = \left(7,~8\right) $ . | 2 |
1350 | Find the sum of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 2 |