Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1251 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(1,~-2\right) $ . | 2 |
1252 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4\right) $ . | 2 |
1253 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~2\right) $ and $ \vec{v_2} = \left(3,~2,~-2\right) $ . | 2 |
1254 | Find the angle between vectors $ \left(-3,~1,~2\right)$ and $\left(1,~0,~2\right)$. | 2 |
1255 | Find the projection of the vector $ \vec{v_1} = \left(-7,~7\right) $ on the vector $ \vec{v_2} = \left(1,~22\right) $. | 2 |
1256 | Find the difference of the vectors $ \vec{v_1} = \left(240,~80\right) $ and $ \vec{v_2} = \left(-110,~287.53\right) $ . | 2 |
1257 | Find the angle between vectors $ \left(2,~0\right)$ and $\left(2,~3\right)$. | 2 |
1258 | Find the angle between vectors $ \left(0,~4\right)$ and $\left(0,~15\right)$. | 2 |
1259 | Find the projection of the vector $ \vec{v_1} = \left(5,~5\right) $ on the vector $ \vec{v_2} = \left(2,~6\right) $. | 2 |
1260 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-18,~3\right) $ and $ \vec{v_2} = \left(1,~6\right) $ . | 2 |
1261 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~0,~0\right) $ and $ \vec{v_2} = \left(-7,~4,~0\right) $ . | 2 |
1262 | Find the sum of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(9,~8\right) $ . | 2 |
1263 | Find the projection of the vector $ \vec{v_1} = \left(-5,~2,~0\right) $ on the vector $ \vec{v_2} = \left(-1,~8,~-4\right) $. | 2 |
1264 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 2 |
1265 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-9,~-2\right) $ . | 2 |
1266 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 2 |
1267 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~9\right) $ . | 2 |
1268 | Find the projection of the vector $ \vec{v_1} = \left(3,~0\right) $ on the vector $ \vec{v_2} = \left(-2,~0\right) $. | 2 |
1269 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-6\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 2 |
1270 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~6,~2\right) $ and $ \vec{v_2} = \left(2,~3,~2\right) $ . | 2 |
1271 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 2 |
1272 | Find the projection of the vector $ \vec{v_1} = \left(6,~3\right) $ on the vector $ \vec{v_2} = \left(5,~9\right) $. | 2 |
1273 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(-8,~-20\right) $ . | 2 |
1274 | Find the angle between vectors $ \left(-2 \sqrt{ 3 },~-2\right)$ and $\left(-4,~-4 \sqrt{ 3 }\right)$. | 2 |
1275 | Find the difference of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 2 |
1276 | Find the sum of the vectors $ \vec{v_1} = \left(0,~-5\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ . | 2 |
1277 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~6\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ . | 2 |
1278 | Find the projection of the vector $ \vec{v_1} = \left(-8,~-8\right) $ on the vector $ \vec{v_2} = \left(-1,~-9\right) $. | 2 |
1279 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ . | 2 |
1280 | Find the difference of the vectors $ \vec{v_1} = \left(330,~0\right) $ and $ \vec{v_2} = \left(170,~-120\right) $ . | 2 |
1281 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 2 |
1282 | Find the angle between vectors $ \left(-3,~1\right)$ and $\left(-9,~3\right)$. | 2 |
1283 | Find the sum of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(7,~1\right) $ . | 2 |
1284 | Find the magnitude of the vector $ \| \vec{v} \| = \left(35,~21\right) $ . | 2 |
1285 | Find the sum of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 2 |
1286 | Find the sum of the vectors $ \vec{v_1} = \left(8,~-4\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 2 |
1287 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 2 |
1288 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~6,~0\right) $ and $ \vec{v_2} = \left(-7,~4,~0\right) $ . | 2 |
1289 | Find the angle between vectors $ \left(-\sqrt{ 3 },~-1\right)$ and $\left(2,~2 \sqrt{ 3 }\right)$. | 2 |
1290 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-3\right) $ and $ \vec{v_2} = \left(-1,~0\right) $ . | 2 |
1291 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1\right) $ . | 2 |
1292 | Determine whether the vectors $ \vec{v_1} = \left(4,~-8\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ are linearly independent or dependent. | 2 |
1293 | Find the difference of the vectors $ \vec{v_1} = \left(8,~9\right) $ and $ \vec{v_2} = \left(9,~7\right) $ . | 2 |
1294 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-6\right) $ . | 2 |
1295 | Find the angle between vectors $ \left(2,~-1.5,~-0.5\right)$ and $\left(0,~1,~0\right)$. | 2 |
1296 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 2 |
1297 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
1298 | Find the sum of the vectors $ \vec{v_1} = \left(0,~3\right) $ and $ \vec{v_2} = \left(1,~-3\right) $ . | 2 |
1299 | Find the difference of the vectors $ \vec{v_1} = \left(18,~-12\right) $ and $ \vec{v_2} = \left(-10,~0\right) $ . | 2 |
1300 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 1 }{ 8 },~\dfrac{ 7 }{ 8 }\right) $. | 2 |