Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 201 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 3 |
| 202 | Find the angle between vectors $ \left(0,~2,~14\right)$ and $\left(0,~2,~-10\right)$. | 3 |
| 203 | Find the difference of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(0,~15\right) $ . | 3 |
| 204 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~-49\right) $ and $ \vec{v_2} = \left(-48,~-72\right) $ . | 3 |
| 205 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-5\right) $ and $ \vec{v_2} = \left(-2,~0\right) $ . | 3 |
| 206 | Find the angle between vectors $ \left(110,~0\right)$ and $\left(110,~240\right)$. | 3 |
| 207 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-4\right) $ . | 3 |
| 208 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 3 |
| 209 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5.2,~2.5,~-4.5\right) $ and $ \vec{v_2} = \left(-3,~4,~-1.25\right) $ . | 3 |
| 210 | Find the angle between vectors $ \left(\dfrac{ 26 }{ 5 },~\dfrac{ 5 }{ 2 },~-\dfrac{ 9 }{ 2 }\right)$ and $\left(-3,~4,~-\dfrac{ 5 }{ 4 }\right)$. | 3 |
| 211 | Find the angle between vectors $ \left(16,~12\right)$ and $\left(32,~25\right)$. | 3 |
| 212 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-190,~321\right) $ . | 3 |
| 213 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 3 |
| 214 | Find the angle between vectors $ \left(50,~57\right)$ and $\left(29,~1\right)$. | 3 |
| 215 | Find the angle between vectors $ \left(25,~4\right)$ and $\left(35,~1\right)$. | 3 |
| 216 | Find the angle between vectors $ \left(25,~24\right)$ and $\left(47,~1\right)$. | 3 |
| 217 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 3 |
| 218 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1\right) $ . | 3 |
| 219 | Find the angle between vectors $ \left(-2,~-7\right)$ and $\left(5,~-9\right)$. | 3 |
| 220 | Find the difference of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 3 |
| 221 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~4 \sqrt{ 3 }\right) $ . | 3 |
| 222 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~10\right) $ and $ \vec{v_2} = \left(6,~12\right) $ . | 3 |
| 223 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ . | 3 |
| 224 | Find the angle between vectors $ \left(11.6881,~32.6073\right)$ and $\left(7.8137,~6.5564\right)$. | 3 |
| 225 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~5\right) $ . | 3 |
| 226 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~23\right) $ . | 3 |
| 227 | Find the difference of the vectors $ \vec{v_1} = \left(2,~2 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(-2,~0\right) $ . | 3 |
| 228 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1\right) $ . | 3 |
| 229 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 3 |
| 230 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(-3,~1\right)$. | 3 |
| 231 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~-18\right) $ and $ \vec{v_2} = \left(-7,~8\right) $ . | 3 |
| 232 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~6\right) $ . | 3 |
| 233 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-2,~4\right) $ and $ \vec{v_2} = \left(0,~-3,~3\right) $ . | 3 |
| 234 | Determine whether the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(8,~2\right) $ are linearly independent or dependent. | 3 |
| 235 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~3\right) $ and $ \vec{v_2} = \left(-1,~2,~-4\right) $ . | 3 |
| 236 | Calculate the dot product of the vectors $ \vec{v_1} = \left(32,~64\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 3 |
| 237 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 49 }{ 100 },~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 27 }{ 500 },~-\dfrac{ 12 }{ 25 }\right) $ . | 3 |
| 238 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ . | 3 |
| 239 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(6,~3\right)$. | 3 |
| 240 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 3 |
| 241 | Find the sum of the vectors $ \vec{v_1} = \left(2,~2 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(6,~0\right) $ . | 3 |
| 242 | Find the projection of the vector $ \vec{v_1} = \left(0,~1,~-3\right) $ on the vector $ \vec{v_2} = \left(2,~-1,~4\right) $. | 3 |
| 243 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~10\right) $ . | 3 |
| 244 | Find the angle between vectors $ \left(0,~4\right)$ and $\left(-5,~1\right)$. | 3 |
| 245 | Find the sum of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 3 |
| 246 | Find the angle between vectors $ \left(9,~8\right)$ and $\left(2,~0\right)$. | 3 |
| 247 | Find the difference of the vectors $ \vec{v_1} = \left(3,~11\right) $ and $ \vec{v_2} = \left(-4,~10\right) $ . | 3 |
| 248 | Find the sum of the vectors $ \vec{v_1} = \left(-24,~4\right) $ and $ \vec{v_2} = \left(13,~14\right) $ . | 3 |
| 249 | Find the angle between vectors $ \left(4,~1\right)$ and $\left(-5,~-4\right)$. | 3 |
| 250 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 3 |
