Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5201 | Find the sum of the vectors $ \vec{v_1} = \left(-30,~0\right) $ and $ \vec{v_2} = \left(19,~-4\right) $ . | 1 |
| 5202 | Find the difference of the vectors $ \vec{v_1} = \left(-11,~-4\right) $ and $ \vec{v_2} = \left(-16,~36\right) $ . | 1 |
| 5203 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~8,~1\right) $ and $ \vec{v_2} = \left(-5,~1,~8\right) $ . | 1 |
| 5204 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~8,~1\right) $ and $ \vec{v_2} = \left(-5,~1,~8\right) $ . | 1 |
| 5205 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~-4\right) $ . | 1 |
| 5206 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-1\right) $ . | 1 |
| 5207 | Find the difference of the vectors $ \vec{v_1} = \left(8,~-1\right) $ and $ \vec{v_2} = \left(-3,~0\right) $ . | 1 |
| 5208 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-17,~-3,~2\right) $ . | 1 |
| 5209 | Find the angle between vectors $ \left(4,~4\right)$ and $\left(3,~-4\right)$. | 1 |
| 5210 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-5\right) $ . | 1 |
| 5211 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~2\right) $ . | 1 |
| 5212 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~2\right) $ on the vector $ \vec{v_2} = \left(-1,~0,~1\right) $. | 1 |
| 5213 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~1,~7\right) $ and $ \vec{v_2} = \left(3,~5,~9\right) $ . | 1 |
| 5214 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~1,~7\right) $ and $ \vec{v_2} = \left(3,~5,~9\right) $ . | 1 |
| 5215 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-1,~-5\right) $ . | 1 |
| 5216 | Find the projection of the vector $ \vec{v_1} = \left(5,~12\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 1 |
| 5217 | Find the angle between vectors $ \left(4,~7\right)$ and $\left(7,~-8\right)$. | 1 |
| 5218 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 1 |
| 5219 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-1\right) $ . | 1 |
| 5220 | Determine whether the vectors $ \vec{v_1} = \left(-4,~5\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ are linearly independent or dependent. | 1 |
| 5221 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ are linearly independent or dependent. | 1 |
| 5222 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~6\right) $ . | 1 |
| 5223 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(9,~-5\right) $ . | 1 |
| 5224 | Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~6\right) $ and $ \vec{v_2} = \left(7,~8\right) $ . | 1 |
| 5225 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(1,~9\right) $ . | 1 |
| 5226 | Find the difference of the vectors $ \vec{v_1} = \left(100,~60\right) $ and $ \vec{v_2} = \left(49,~56\right) $ . | 1 |
| 5227 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-1\right) $ and $ \vec{v_2} = \left(7,~-6\right) $ . | 1 |
| 5228 | Find the difference of the vectors $ \vec{v_1} = \left(-9,~12\right) $ and $ \vec{v_2} = \left(8,~-4\right) $ . | 1 |
| 5229 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~12\right) $ . | 1 |
| 5230 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~12\right) $ . | 1 |
| 5231 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~3\right) $ . | 1 |
| 5232 | Find the sum of the vectors $ \vec{v_1} = \left(100,~0,~300\right) $ and $ \vec{v_2} = \left(-70,~-40,~-240\right) $ . | 1 |
| 5233 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~5,~0\right) $ and $ \vec{v_2} = \left(-60,~40,~20\right) $ . | 1 |
| 5234 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~5,~0\right) $ and $ \vec{v_2} = \left(-60,~40,~20\right) $ . | 1 |
| 5235 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~5,~-2\right) $ and $ \vec{v_2} = \left(80,~40,~-30\right) $ . | 1 |
| 5236 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-6\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 1 |
| 5237 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~8\right) $ and $ \vec{v_2} = \left(8,~8\right) $ . | 1 |
| 5238 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 1 |
| 5239 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~8\right) $ and $ \vec{v_2} = \left(-9,~3\right) $ . | 1 |
| 5240 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-1,~2\right) $ . | 1 |
| 5241 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(-3,~8\right) $ . | 1 |
| 5242 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ . | 1 |
| 5243 | Determine whether the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-2,~8\right) $ are linearly independent or dependent. | 1 |
| 5244 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~6,~-5\right) $ and $ \vec{v_2} = \left(3,~-4,~8\right) $ . | 1 |
| 5245 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 1 |
| 5246 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 5247 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 5248 | Find the angle between vectors $ \left(3,~0\right)$ and $\left(9,~2\right)$. | 1 |
| 5249 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~0,~-3\right) $ . | 1 |
| 5250 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~0,~-3\right) $ . | 1 |
