Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4201 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-10,~-8\right) $ . | 1 |
| 4202 | Determine whether the vectors $ \vec{v_1} = \left(-10,~-8\right) $ and $ \vec{v_2} = \left(20,~16\right) $ are linearly independent or dependent. | 1 |
| 4203 | Find the angle between vectors $ \left(-10,~-8\right)$ and $\left(20,~16\right)$. | 1 |
| 4204 | Find the angle between vectors $ \left(3,~7,~10\right)$ and $\left(1,~10,~8\right)$. | 1 |
| 4205 | Find the angle between vectors $ \left(2,~2,~4\right)$ and $\left(1,~7,~1\right)$. | 1 |
| 4206 | Find the angle between vectors $ \left(3,~5,~-7\right)$ and $\left(-3,~4,~-2\right)$. | 1 |
| 4207 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~5\right) $ . | 1 |
| 4208 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~3\right) $ . | 1 |
| 4209 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~8\right) $ . | 1 |
| 4210 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 625 },~0,~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 1 }{ 35 },~0\right) $ . | 1 |
| 4211 | Find the angle between vectors $ \left(\sqrt{ 2 },~4,~3\right)$ and $\left(2,~4,~9\right)$. | 1 |
| 4212 | Determine whether the vectors $ \vec{v_1} = \left(\sqrt{ 2 },~4,~3\right) $, $ \vec{v_2} = \left(2,~4,~9\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 4213 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-1,~3\right) $ and $ \vec{v_2} = \left(-3,~0,~1\right) $ . | 1 |
| 4214 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~8,~-6\right) $ and $ \vec{v_2} = \left(7,~4,~-1\right) $ . | 1 |
| 4215 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~8,~-10\right) $ and $ \vec{v_2} = \left(16,~-38,~-40\right) $ . | 1 |
| 4216 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9,~8,~-10\right) $ and $ \vec{v_2} = \left(4,~8,~-6\right) $ . | 1 |
| 4217 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~4,~-1\right) $ and $ \vec{v_2} = \left(32,~14,~40\right) $ . | 1 |
| 4218 | Determine whether the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ are linearly independent or dependent. | 1 |
| 4219 | Determine whether the vectors $ \vec{v_1} = \left(1,~0,~0\right) $, $ \vec{v_2} = \left(1,~0,~1\right) $ and $ \vec{v_3} = \left(1,~1,~1\right)$ are linearly independent or dependent. | 1 |
| 4220 | Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(4,~4\right) $ . | 1 |
| 4221 | Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ . | 1 |
| 4222 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ . | 1 |
| 4223 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 1 |
| 4224 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1,~-3\right) $ and $ \vec{v_2} = \left(1,~2,~-3\right) $ . | 1 |
| 4225 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-1,~0\right) $ are linearly independent or dependent. | 1 |
| 4226 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5,~-6\right) $ and $ \vec{v_2} = \left(2,~-3,~4\right) $ . | 1 |
| 4227 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-15,~-24\right) $ and $ \vec{v_2} = \left(7,~6,~-5\right) $ . | 1 |
| 4228 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(3,~2,~1\right) $ . | 1 |
| 4229 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(3,~2,~1\right)$. | 1 |
| 4230 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(3,~2,~1\right) $ . | 1 |
| 4231 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(3,~2,~1\right) $ . | 1 |
| 4232 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~4\right) $ . | 1 |
| 4233 | 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(7,~8,~9\right)$ are linearly independent or dependent. | 1 |
| 4234 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-15,~-8\right) $ . | 1 |
| 4235 | | 1 |
| 4236 | Determine whether the vectors $ \vec{v_1} = \left(0,~1,~2\right) $, $ \vec{v_2} = \left(0,~3,~5\right) $ and $ \vec{v_3} = \left(0,~2,~5\right)$ are linearly independent or dependent. | 1 |
| 4237 | Determine whether the vectors $ \vec{v_1} = \left(0,~1,~2\right) $, $ \vec{v_2} = \left(0,~3,~5\right) $ and $ \vec{v_3} = \left(0,~2,~5\right)$ are linearly independent or dependent. | 1 |
| 4238 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~6\right) $ . | 1 |
| 4239 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 4139 }{ 200 },~\dfrac{ 2143 }{ 250 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 399 }{ 40 },~\dfrac{ 3748 }{ 125 }\right) $ . | 1 |
| 4240 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~4\right) $ . | 1 |
| 4241 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~-3,~-2\right) $ . | 1 |
| 4242 | Find the projection of the vector $ \vec{v_1} = \left(0,~1,~\sqrt{ 3 }\right) $ on the vector $ \vec{v_2} = \left(-1,~\sqrt{ 3 },~-1\right) $. | 1 |
| 4243 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~6\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 1 |
| 4244 | Find the angle between vectors $ \left(4,~6\right)$ and $\left(2,~3\right)$. | 1 |
| 4245 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(-1,~-4,~2\right) $ . | 1 |
| 4246 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~3,~3\right) $ and $ \vec{v_2} = \left(4,~5,~6\right) $ . | 1 |
| 4247 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(-3,~7\right) $ . | 1 |
| 4248 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
| 4249 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~-7\right) $ . | 1 |
| 4250 | Find the magnitude of the vector $ \| \vec{v} \| = \left(34,~90\right) $ . | 1 |
