Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1201 | Calculate the dot product of the vectors $ \vec{v_1} = \left(30,~-6\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 2 |
1202 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~2\right) $ . | 2 |
1203 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 16 }{ 5 },~\dfrac{ 24 }{ 5 }\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 2 |
1204 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~1\right) $ . | 2 |
1205 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 97 }{ 10 },~\dfrac{ 49 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 5 },~\dfrac{ 34 }{ 5 }\right) $ . | 2 |
1206 | Find the difference of the vectors $ \vec{v_1} = \left(5,~7\right) $ and $ \vec{v_2} = \left(7,~3\right) $ . | 2 |
1207 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 2 |
1208 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 2 |
1209 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-3\right) $ and $ \vec{v_2} = \left(4,~0\right) $ . | 2 |
1210 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-11,~5\right) $ . | 2 |
1211 | Find the angle between vectors $ \left(-1,~2\right)$ and $\left(1,~1\right)$. | 2 |
1212 | Find the projection of the vector $ \vec{v_1} = \left(-6,~4\right) $ on the vector $ \vec{v_2} = \left(-3,~6\right) $. | 2 |
1213 | Find the angle between vectors $ \left(3,~5,~-7\right)$ and $\left(-3,~4,~-2\right)$. | 2 |
1214 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0\right) $ . | 2 |
1215 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(10,~5\right) $ are linearly independent or dependent. | 2 |
1216 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~-19\right) $ . | 2 |
1217 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~4,~16\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 2 |
1218 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~1\right) $ . | 2 |
1219 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2\right) $ . | 2 |
1220 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 2 |
1221 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 173 }{ 10 },~10\right) $ . | 2 |
1222 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~7\right) $ . | 2 |
1223 | Find the angle between vectors $ \left(4,~0\right)$ and $\left(2,~5\right)$. | 2 |
1224 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(\dfrac{ 22 }{ 5 },~-\dfrac{ 23 }{ 5 }\right) $ . | 2 |
1225 | Calculate the dot product of the vectors $ \vec{v_1} = \left(11,~1\right) $ and $ \vec{v_2} = \left(11,~1\right) $ . | 2 |
1226 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~5\right) $ . | 2 |
1227 | Find the difference of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 2 |
1228 | Find the angle between vectors $ \left(\dfrac{ 173 }{ 10 },~10\right)$ and $\left(-\dfrac{ 63 }{ 10 },~\dfrac{ 68 }{ 5 }\right)$. | 2 |
1229 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(7,~17\right) $ . | 2 |
1230 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~6\right) $ . | 2 |
1231 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2\right) $ . | 2 |
1232 | Find the angle between vectors $ \left(-4,~3\right)$ and $\left(5,~7\right)$. | 2 |
1233 | Find the sum of the vectors $ \vec{v_1} = \left(0,~3\right) $ and $ \vec{v_2} = \left(3,~7\right) $ . | 2 |
1234 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 2 |
1235 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~6\right) $ . | 2 |
1236 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~\sqrt{ 8 }\right) $ . | 2 |
1237 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(1,~6\right) $ . | 2 |
1238 | Find the difference of the vectors $ \vec{v_1} = \left(7,~5\right) $ and $ \vec{v_2} = \left(-2,~-3\right) $ . | 2 |
1239 | Find the angle between vectors $ \left(-2,~0,~-3\right)$ and $\left(1,~-3,~-1\right)$. | 2 |
1240 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~2\right) $ . | 2 |
1241 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(-7,~7\right) $ . | 2 |
1242 | Find the angle between vectors $ \left(4,~-8\right)$ and $\left(-2,~4\right)$. | 2 |
1243 | Find the angle between vectors $ \left(-1,~6\right)$ and $\left(2,~-3\right)$. | 2 |
1244 | Find the sum of the vectors $ \vec{v_1} = \left(5,~5\right) $ and $ \vec{v_2} = \left(2,~6\right) $ . | 2 |
1245 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~1\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ . | 2 |
1246 | Find the angle between vectors $ \left(-1,~5,~6\right)$ and $\left(2,~3,~-1\right)$. | 2 |
1247 | Find the angle between vectors $ \left(0,~4\right)$ and $\left(4,~1\right)$. | 2 |
1248 | Find the angle between vectors $ \left(-1,~8\right)$ and $\left(0,~-1\right)$. | 2 |
1249 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(2,~-6\right) $ . | 2 |
1250 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~8\right) $ and $ \vec{v_2} = \left(5,~-5\right) $ . | 2 |