Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3201 | Find the projection of the vector $ \vec{v_1} = \left(-4,~3\right) $ on the vector $ \vec{v_2} = \left(3,~-5\right) $. | 1 |
| 3202 | Find the projection of the vector $ \vec{v_1} = \left(-4,~3\right) $ on the vector $ \vec{v_2} = \left(3,~-6\right) $. | 1 |
| 3203 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(3,~-6\right) $ . | 1 |
| 3204 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(6,~-12\right) $ . | 1 |
| 3205 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-6\right) $ and $ \vec{v_2} = \left(-6,~-8\right) $ . | 1 |
| 3206 | Find the angle between vectors $ \left(-4,~3\right)$ and $\left(-4,~3\right)$. | 1 |
| 3207 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-0.3816,~-1.9633\right) $ . | 1 |
| 3208 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-5\right) $ . | 1 |
| 3209 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-2\right) $ . | 1 |
| 3210 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~7\right) $ . | 1 |
| 3211 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~7\right) $ . | 1 |
| 3212 | Find the projection of the vector $ \vec{v_1} = \left(-4,~7\right) $ on the vector $ \vec{v_2} = \left(24,~-8\right) $. | 1 |
| 3213 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 7 }{ 3 },~-\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(14,~3\right) $ . | 1 |
| 3214 | Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(6,~9\right) $ . | 1 |
| 3215 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-4\right) $ . | 1 |
| 3216 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-1\right) $ and $ \vec{v_2} = \left(1,~-6\right) $ . | 1 |
| 3217 | Find the projection of the vector $ \vec{v_1} = \left(-2,~-1\right) $ on the vector $ \vec{v_2} = \left(1,~-6\right) $. | 1 |
| 3218 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 3219 | Find the sum of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 1 |
| 3220 | Find the sum of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(1,~-6\right) $ . | 1 |
| 3221 | Find the sum of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(-5,~-1\right) $ . | 1 |
| 3222 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~3\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 1 |
| 3223 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(-3,~-1\right) $ . | 1 |
| 3224 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
| 3225 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~4\right) $ and $ \vec{v_2} = \left(2,~3,~5\right) $ . | 1 |
| 3226 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~4\right) $, $ \vec{v_2} = \left(2,~3,~5\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 3227 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(-1,~-1\right) $ . | 1 |
| 3228 | Find the projection of the vector $ \vec{v_1} = \left(-2,~-3,~5\right) $ on the vector $ \vec{v_2} = \left(-6,~3,~4\right) $. | 1 |
| 3229 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-3,~5\right) $ and $ \vec{v_2} = \left(-6,~3,~4\right) $ . | 1 |
| 3230 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-3,~5\right) $ and $ \vec{v_2} = \left(-6,~3,~4\right) $ . | 1 |
| 3231 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-1,~1\right) $ and $ \vec{v_2} = \left(-1,~1,~1\right) $ . | 1 |
| 3232 | Find the angle between vectors $ \left(0,~-1,~1\right)$ and $\left(-1,~1,~1\right)$. | 1 |
| 3233 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~2\right) $ . | 1 |
| 3234 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~-2\right) $ and $ \vec{v_2} = \left(3,~-1,~3\right) $ . | 1 |
| 3235 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-15,~-9\right) $ and $ \vec{v_2} = \left(-3,~2,~2\right) $ . | 1 |
| 3236 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~2\right) $ and $ \vec{v_2} = \left(4,~-15,~-9\right) $ . | 1 |
| 3237 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~3\right) $ and $ \vec{v_2} = \left(-3,~2,~2\right) $ . | 1 |
| 3238 | Determine whether the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $, $ \vec{v_2} = \left(3,~1,~0\right) $ and $ \vec{v_3} = \left(-1,~2,~-3\right)$ are linearly independent or dependent. | 1 |
| 3239 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~-2\right) $ and $ \vec{v_2} = \left(-8,~-15,~3\right) $ . | 1 |
| 3240 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
| 3241 | Find the difference of the vectors $ \vec{v_1} = \left(-24,~21\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ . | 1 |
| 3242 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2,~-3\right) $ and $ \vec{v_2} = \left(2,~-2,~1\right) $ . | 1 |
| 3243 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~0\right) $ and $ \vec{v_2} = \left(-5,~3,~0\right) $ . | 1 |
| 3244 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-4\right) $ and $ \vec{v_2} = \left(7,~4\right) $ . | 1 |
| 3245 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~3,~-4\right) $ and $ \vec{v_2} = \left(2,~1,~3\right) $ . | 1 |
| 3246 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-7\right) $ and $ \vec{v_2} = \left(6,~-1\right) $ . | 1 |
| 3247 | Find the angle between vectors $ \left(-\dfrac{ 1 }{ 2 },~-\dfrac{ 1 }{ 2 },~1\right)$ and $\left(-1,~0,~1\right)$. | 1 |
| 3248 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1000,~2000,~3000\right) $ . | 1 |
| 3249 | Find the sum of the vectors $ \vec{v_1} = \left(4,~6\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 1 |
| 3250 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2,~0\right) $ . | 1 |
