Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6151 | Find the angle between vectors $ \left(0,~-4,~-4\right)$ and $\left(0,~-2,~-14\right)$. | 1 |
| 6152 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(0,~1,~-1\right) $ . | 1 |
| 6153 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
| 6154 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~-3\right) $ and $ \vec{v_2} = \left(-19,~5\right) $ . | 1 |
| 6155 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-3\right) $ and $ \vec{v_2} = \left(-19,~5\right) $ . | 1 |
| 6156 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~-5\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ . | 1 |
| 6157 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~1\right) $ . | 1 |
| 6158 | Find the projection of the vector $ \vec{v_1} = \left(-2,~3\right) $ on the vector $ \vec{v_2} = \left(3,~4\right) $. | 1 |
| 6159 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
| 6160 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
| 6161 | Find the angle between vectors $ \left(7,~-2\right)$ and $\left(-12,~-5\right)$. | 1 |
| 6162 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 13 }{ 10 },~\dfrac{ 481 }{ 100 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 37 }{ 5 },~2\right) $ are linearly independent or dependent. | 1 |
| 6163 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 13 }{ 10 },~\dfrac{ 481 }{ 100 }\right) $ on the vector $ \vec{v_2} = \left(-\dfrac{ 37 }{ 5 },~2\right) $. | 1 |
| 6164 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
| 6165 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right) $ . | 1 |
| 6166 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~5\right) $ . | 1 |
| 6167 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~6\right) $ . | 1 |
| 6168 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-4,~2\right) $ and $ \vec{v_2} = \left(4,~0,~-1\right) $ . | 1 |
| 6169 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 99 }{ 50 },~-\dfrac{ 587 }{ 100 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 413 }{ 100 },~\dfrac{ 68 }{ 25 },~0\right) $ . | 1 |
| 6170 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 3 },~\dfrac{ 2 }{ 3 },~\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 2 }{ 3 },~\dfrac{ 2 }{ 3 },~-\dfrac{ 1 }{ 3 }\right) $ . | 1 |
| 6171 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~0\right) $ . | 1 |
| 6172 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~0\right) $ . | 1 |
| 6173 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-24,~6\right) $ . | 1 |
| 6174 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-24,~6\right) $ . | 1 |
| 6175 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 71 }{ 10 },~-3\right) $ . | 1 |
| 6176 | Find the angle between vectors $ \left(-5,~5\right)$ and $\left(1,~1\right)$. | 1 |
| 6177 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 6178 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 6179 | Determine whether the vectors $ \vec{v_1} = \left(0,~1,~1\right) $, $ \vec{v_2} = \left(1,~1,~2\right) $ and $ \vec{v_3} = \left(2,~2,~2\right)$ are linearly independent or dependent. | 1 |
| 6180 | Find the angle between vectors $ \left(3,~0,~-1\right)$ and $\left(-4,~5,~2\right)$. | 1 |
| 6181 | Find the sum of the vectors $ \vec{v_1} = \left(0,~1,~2\right) $ and $ \vec{v_2} = \left(1,~1,~3\right) $ . | 1 |
| 6182 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1,~3\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 6183 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 3 },~-\dfrac{ 1 }{ 3 },~\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 6184 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 3 },~-\dfrac{ 1 }{ 3 },~\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(1,~-1,~2\right) $ . | 1 |
| 6185 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 17 }{ 10 },~-\dfrac{ 19 }{ 5 },~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 53 }{ 10 },~0\right) $ . | 1 |
| 6186 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1.8,~-3.4,~0\right) $ and $ \vec{v_2} = \left(0,~5.6,~0\right) $ . | 1 |
| 6187 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(1,~-1,~-1\right) $ . | 1 |
| 6188 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(0,~-1,~-1\right) $ . | 1 |
| 6189 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(0,~-1,~1\right) $ . | 1 |
| 6190 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1.7,~-3.4,~0\right) $ and $ \vec{v_2} = \left(0,~5.3,~0\right) $ . | 1 |
| 6191 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-8\right) $ and $ \vec{v_2} = \left(-5,~-3\right) $ . | 1 |
| 6192 | Find the sum of the vectors $ \vec{v_1} = \left(-20,~-36\right) $ and $ \vec{v_2} = \left(63,~-49\right) $ . | 1 |
| 6193 | Find the difference of the vectors $ \vec{v_1} = \left(25,~45\right) $ and $ \vec{v_2} = \left(-18,~14\right) $ . | 1 |
| 6194 | Find the difference of the vectors $ \vec{v_1} = \left(-20,~36\right) $ and $ \vec{v_2} = \left(63,~49\right) $ . | 1 |
| 6195 | Find the sum of the vectors $ \vec{v_1} = \left(-20,~36\right) $ and $ \vec{v_2} = \left(63,~49\right) $ . | 1 |
| 6196 | Find the difference of the vectors $ \vec{v_1} = \left(-25,~45\right) $ and $ \vec{v_2} = \left(18,~-14\right) $ . | 1 |
| 6197 | Find the projection of the vector $ \vec{v_1} = \left(5,~6\right) $ on the vector $ \vec{v_2} = \left(8,~1\right) $. | 1 |
| 6198 | Find the difference of the vectors $ \vec{v_1} = \left(5,~6\right) $ and $ \vec{v_2} = \left(8,~1\right) $ . | 1 |
| 6199 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~2\right) $ . | 1 |
| 6200 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
