Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6201 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~2\right) $ . | 1 |
| 6202 | 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 |
| 6203 | Find the angle between vectors $ \left(5,~3\right)$ and $\left(8,~9\right)$. | 1 |
| 6204 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~2\right) $ . | 1 |
| 6205 | Find the angle between vectors $ \left(1,~1\right)$ and $\left(4,~4\right)$. | 1 |
| 6206 | Find the angle between vectors $ \left(54.9123,~23.9363\right)$ and $\left(54.9276,~23.9704\right)$. | 1 |
| 6207 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~\sqrt{ 7 }\right) $ and $ \vec{v_2} = \left(64,~36\right) $ . | 1 |
| 6208 | Find the difference of the vectors $ \vec{v_1} = \left(-8,~\sqrt{ 7 }\right) $ and $ \vec{v_2} = \left(64,~36\right) $ . | 1 |
| 6209 | Find the angle between vectors $ \left(-8,~\sqrt{ 7 }\right)$ and $\left(64,~36\right)$. | 1 |
| 6210 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ . | 1 |
| 6211 | Find the sum of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-1,~1,~2\right) $ . | 1 |
| 6212 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-1,~1,~2\right) $ . | 1 |
| 6213 | Determine whether the vectors $ \vec{v_1} = \left(2,~7,~1\right) $, $ \vec{v_2} = \left(0,~14,~2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 6214 | Determine whether the vectors $ \vec{v_1} = \left(6,~9,~15\right) $, $ \vec{v_2} = \left(2,~3,~5\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 6215 | Determine whether the vectors $ \vec{v_1} = \left(1,~6,~4\right) $, $ \vec{v_2} = \left(0,~3,~2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 6216 | Find the angle between vectors $ \left(-7,~-6\right)$ and $\left(5,~-1\right)$. | 1 |
| 6217 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~5\right) $ . | 1 |
| 6218 | Find the difference of the vectors $ \vec{v_1} = \left(54.9194,~23.95\right) $ and $ \vec{v_2} = \left(54.9119,~23.9361\right) $ . | 1 |
| 6219 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~1\right) $ . | 1 |
| 6220 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 400 },~\dfrac{ 139 }{ 10000 }\right) $ and $ \vec{v_2} = \left(0.4186,~0.9082\right) $ . | 1 |
| 6221 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 400 },~\dfrac{ 139 }{ 10000 }\right) $ and $ \vec{v_2} = \left(-0.9082,~0.4186\right) $ . | 1 |
| 6222 | Find the difference of the vectors $ \vec{v_1} = \left(54.9122,~23.9347\right) $ and $ \vec{v_2} = \left(54.9119,~23.9361\right) $ . | 1 |
| 6223 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 10000 },~-\dfrac{ 7 }{ 5000 }\right) $ and $ \vec{v_2} = \left(0.4186,~0.9082\right) $ . | 1 |
| 6224 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ . | 1 |
| 6225 | Determine whether the vectors $ \vec{v_1} = \left(30,~-30,~30\right) $, $ \vec{v_2} = \left(60,~60,~-30\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 6226 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ . | 1 |
| 6227 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-12\right) $ . | 1 |
| 6228 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ . | 1 |
| 6229 | Find the projection of the vector $ \vec{v_1} = \left(10,~5\right) $ on the vector $ \vec{v_2} = \left(5,~10\right) $. | 1 |
| 6230 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(-4,~-2\right)$. | 1 |
| 6231 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 1 |
| 6232 | Find the projection of the vector $ \vec{v_1} = \left(2,~5\right) $ on the vector $ \vec{v_2} = \left(-4,~-2\right) $. | 1 |
| 6233 | Determine whether the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ are linearly independent or dependent. | 1 |
| 6234 | Find the sum of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 1 |
| 6235 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9.88,~0,~0\right) $ and $ \vec{v_2} = \left(2.1,~-2.6,~0\right) $ . | 1 |
| 6236 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~2\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 1 |
| 6237 | Calculate the cross product of the vectors $ \vec{v_1} = \left(11.44,~0,~0\right) $ and $ \vec{v_2} = \left(1.8,~-3.4,~0\right) $ . | 1 |
| 6238 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(-1,~3\right)$. | 1 |
| 6239 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~4\right) $ and $ \vec{v_2} = \left(-3,~18\right) $ . | 1 |
| 6240 | Find the projection of the vector $ \vec{v_1} = \left(2,~-5\right) $ on the vector $ \vec{v_2} = \left(1,~-1\right) $. | 1 |
| 6241 | Find the angle between vectors $ \left(2,~3\right)$ and $\left(6,~-4\right)$. | 1 |
| 6242 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(3,~4\right)$. | 1 |
| 6243 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~3\right) $ . | 1 |
| 6244 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-1,~6\right) $ . | 1 |
| 6245 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-3\right) $ . | 1 |
| 6246 | Find the angle between vectors $ \left(4,~7\right)$ and $\left(-2,~6\right)$. | 1 |
| 6247 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~3\right) $ and $ \vec{v_2} = \left(5,~-1,~2\right) $ . | 1 |
| 6248 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~6\right) $ and $ \vec{v_2} = \left(11,~11,~22\right) $ . | 1 |
| 6249 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~2\right) $ and $ \vec{v_2} = \left(-1,~4,~-3\right) $ . | 1 |
| 6250 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $ and $ \vec{v_2} = \left(-5,~-8,~-3\right) $ . | 1 |
