Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5151 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $, $ \vec{v_2} = \left(4,~-5,~6\right) $ and $ \vec{v_3} = \left(3,~2,~-1\right)$ are linearly independent or dependent. | 1 |
| 5152 | Find the angle between vectors $ \left(5,~3,~5\right)$ and $\left(1,~-3,~-2\right)$. | 1 |
| 5153 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~6,~-2\right) $ and $ \vec{v_2} = \left(5,~1,~-4\right) $ . | 1 |
| 5154 | Find the sum of the vectors $ \vec{v_1} = \left(3,~6,~-2\right) $ and $ \vec{v_2} = \left(5,~1,~-4\right) $ . | 1 |
| 5155 | Find the difference of the vectors $ \vec{v_1} = \left(3,~6,~-2\right) $ and $ \vec{v_2} = \left(5,~1,~-4\right) $ . | 1 |
| 5156 | Find the angle between vectors $ \left(5,~3,~5\right)$ and $\left(3,~2,~2\right)$. | 1 |
| 5157 | Find the angle between vectors $ \left(5,~3,~5\right)$ and $\left(-10,~0,~10\right)$. | 1 |
| 5158 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~-3\right) $ on the vector $ \vec{v_2} = \left(4,~-5,~6\right) $. | 1 |
| 5159 | Find the angle between vectors $ \left(5,~3,~5\right)$ and $\left(-2,~1,~-1\right)$. | 1 |
| 5160 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~-3\right) $ . | 1 |
| 5161 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~1,~0\right) $ and $ \vec{v_2} = \left(2,~9,~0\right) $ . | 1 |
| 5162 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 1 |
| 5163 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~5\right) $ and $ \vec{v_2} = \left(6,~3,~2\right) $ . | 1 |
| 5164 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $ and $ \vec{v_2} = \left(4,~5,~-6\right) $ . | 1 |
| 5165 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $ and $ \vec{v_2} = \left(4,~-5,~6\right) $ . | 1 |
| 5166 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~5,~3\right) $ and $ \vec{v_2} = \left(4,~-4,~3\right) $ . | 1 |
| 5167 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~1,~3\right) $ . | 1 |
| 5168 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 1 |
| 5169 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-2\right) $ . | 1 |
| 5170 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-1,~-5\right) $ . | 1 |
| 5171 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 1 |
| 5172 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~1,~1\right) $ and $ \vec{v_2} = \left(-3,~3,~-2\right) $ . | 1 |
| 5173 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4,~-5\right) $ . | 1 |
| 5174 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~2,~-3\right) $ and $ \vec{v_2} = \left(3,~-2,~2\right) $ . | 1 |
| 5175 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-9,~6,~-6\right) $ and $ \vec{v_2} = \left(3,~-2,~2\right) $ . | 1 |
| 5176 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~8\right) $ . | 1 |
| 5177 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~5\right) $ and $ \vec{v_2} = \left(6,~2,~5\right) $ . | 1 |
| 5178 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~2\right) $ on the vector $ \vec{v_2} = \left(-2,~3,~1\right) $. | 1 |
| 5179 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~5\right) $ . | 1 |
| 5180 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~3,~4\right) $ and $ \vec{v_2} = \left(-2,~1,~5\right) $ . | 1 |
| 5181 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~3,~4\right) $ and $ \vec{v_2} = \left(-2,~1,~5\right) $ . | 1 |
| 5182 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~6\right) $ . | 1 |
| 5183 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-8\right) $ . | 1 |
| 5184 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~2\right) $ . | 1 |
| 5185 | Determine whether the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(-10,~-4\right) $ are linearly independent or dependent. | 1 |
| 5186 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~2,~1\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 5187 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~5,~-1\right) $ . | 1 |
| 5188 | Find the angle between vectors $ \left(1,~-2\right)$ and $\left(2,~2\right)$. | 1 |
| 5189 | Find the projection of the vector $ \vec{v_1} = \left(3,~4\right) $ on the vector $ \vec{v_2} = \left(8,~6\right) $. | 1 |
| 5190 | Find the projection of the vector $ \vec{v_1} = \left(8,~6\right) $ on the vector $ \vec{v_2} = \left(3,~4\right) $. | 1 |
| 5191 | Find the angle between vectors $ \left(-2,~5\right)$ and $\left(4,~12\right)$. | 1 |
| 5192 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~8\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 1 |
| 5193 | Find the projection of the vector $ \vec{v_1} = \left(-7,~-3\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 1 |
| 5194 | Determine whether the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent. | 1 |
| 5195 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~8\right) $ . | 1 |
| 5196 | Determine whether the vectors $ \vec{v_1} = \left(9,~8\right) $ and $ \vec{v_2} = \left(2,~0\right) $ are linearly independent or dependent. | 1 |
| 5197 | Find the sum of the vectors $ \vec{v_1} = \left(4,~18\right) $ and $ \vec{v_2} = \left(30,~-20\right) $ . | 1 |
| 5198 | Find the angle between vectors $ \left(1,~0\right)$ and $\left(1,~1\right)$. | 1 |
| 5199 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 1 |
| 5200 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~0\right) $ and $ \vec{v_2} = \left(4,~-1,~2\right) $ . | 1 |
