Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 151 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-10,~2\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 4 |
| 152 | Calculate the dot product of the vectors $ \vec{v_1} = \left(11,~1\right) $ and $ \vec{v_2} = \left(1,~11\right) $ . | 4 |
| 153 | Find the angle between vectors $ \left(-2,~2\right)$ and $\left(0,~-4\right)$. | 4 |
| 154 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 4 |
| 155 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1\right) $ . | 4 |
| 156 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~5\right) $ are linearly independent or dependent. | 4 |
| 157 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~0\right) $ . | 4 |
| 158 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(6,~-2\right) $ . | 4 |
| 159 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4\right) $ . | 4 |
| 160 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-7,~2\right) $ . | 4 |
| 161 | Find the sum of the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 4 |
| 162 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 4 |
| 163 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(8,~-2\right) $ . | 4 |
| 164 | Find the angle between vectors $ \left(-6,~3\right)$ and $\left(7,~-1\right)$. | 4 |
| 165 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-3,~-3\right) $ . | 4 |
| 166 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~-3\right) $ and $ \vec{v_2} = \left(3,~-8\right) $ . | 4 |
| 167 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 4 |
| 168 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 4 |
| 169 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 4 |
| 170 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 4 |
| 171 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~0\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 4 |
| 172 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~3\right) $ and $ \vec{v_2} = \left(-3,~6\right) $ . | 4 |
| 173 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 4 |
| 174 | Find the angle between vectors $ \left(5 \sqrt{ 2 },~-3\right)$ and $\left(17,~-26\right)$. | 3 |
| 175 | Determine whether the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ are linearly independent or dependent. | 3 |
| 176 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~-49\right) $ and $ \vec{v_2} = \left(-48,~-72\right) $ . | 3 |
| 177 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~3\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ . | 3 |
| 178 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-5\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 3 |
| 179 | Find the projection of the vector $ \vec{v_1} = \left(-3,~-6\right) $ on the vector $ \vec{v_2} = \left(-5,~2\right) $. | 3 |
| 180 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(3,~-3\right) $ . | 3 |
| 181 | Find the angle between vectors $ \left(0,~2,~14\right)$ and $\left(0,~2,~-10\right)$. | 3 |
| 182 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~5\right) $ . | 3 |
| 183 | Find the difference of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(0,~15\right) $ . | 3 |
| 184 | Determine whether the vectors $ \vec{v_1} = \left(3,~12,~-21\right) $, $ \vec{v_2} = \left(2,~0,~4\right) $ and $ \vec{v_3} = \left(0,~-10,~20\right)$ are linearly independent or dependent. | 3 |
| 185 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~-4\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ . | 3 |
| 186 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(6,~-2\right) $ . | 3 |
| 187 | Find the difference of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 3 |
| 188 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~3\right) $ . | 3 |
| 189 | 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 |
| 190 | Find the projection of the vector $ \vec{v_1} = \left(0,~1,~-3\right) $ on the vector $ \vec{v_2} = \left(-64,~-2,~30\right) $. | 3 |
| 191 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 3 |
| 192 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-5\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 3 |
| 193 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~7\right) $ . | 3 |
| 194 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~0\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 3 |
| 195 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1\right) $ . | 3 |
| 196 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~1\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 3 |
| 197 | Determine whether the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~2\right) $ are linearly independent or dependent. | 3 |
| 198 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 10000 },~-\dfrac{ 7 }{ 5000 }\right) $ and $ \vec{v_2} = \left(-0.9082,~0.4186\right) $ . | 3 |
| 199 | Find the projection of the vector $ \vec{v_1} = \left(13,~8\right) $ on the vector $ \vec{v_2} = \left(5,~-3\right) $. | 3 |
| 200 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-4\right) $ and $ \vec{v_2} = \left(6,~-8\right) $ . | 3 |
