Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6301 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
6302 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~18\right) $ . | 1 |
6303 | Find the angle between vectors $ \left(4,~-1\right)$ and $\left(-4,~0\right)$. | 1 |
6304 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 1 |
6305 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~1,~0\right) $ and $ \vec{v_2} = \left(1,~6,~7\right) $ . | 1 |
6306 | Find the difference of the vectors $ \vec{v_1} = \left(5,~-3\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
6307 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~3\right) $ and $ \vec{v_2} = \left(7,~0,~0\right) $ . | 1 |
6308 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 4 },~-1\right)$ and $\left(\dfrac{ 1 }{ 4 },~1\right)$. | 1 |
6309 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4\right) $ . | 1 |
6310 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~5\right) $ and $ \vec{v_2} = \left(6,~3,~2\right) $ . | 1 |
6311 | Find the angle between vectors $ \left(-6,~6\right)$ and $\left(-7,~-6\right)$. | 1 |
6312 | Determine whether the vectors $ \vec{v_1} = \left(9,~8\right) $ and $ \vec{v_2} = \left(2,~0\right) $ are linearly independent or dependent. | 1 |
6313 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~9,~6\right) $ and $ \vec{v_2} = \left(8,~3,~-2\right) $ . | 1 |
6314 | Determine whether the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(1,~2\right) $ are linearly independent or dependent. | 1 |
6315 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~3\right) $, $ \vec{v_2} = \left(0,~1,~4\right) $ and $ \vec{v_3} = \left(2,~-1,~1\right)$ are linearly independent or dependent. | 1 |
6316 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 8 },~\dfrac{ 7 }{ 8 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
6317 | Find the angle between vectors $ \left(-1,~2\right)$ and $\left(1,~-1\right)$. | 1 |
6318 | Find the angle between vectors $ \left(0,~2,~-10\right)$ and $\left(0,~-4,~-4\right)$. | 1 |
6319 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~2\right) $ and $ \vec{v_2} = \left(-1,~4,~-3\right) $ . | 1 |
6320 | Find the projection of the vector $ \vec{v_1} = \left(0,~0,~1\right) $ on the vector $ \vec{v_2} = \left(0,~1,~0\right) $. | 1 |
6321 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 1 |
6322 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 7 },~\dfrac{ 5 }{ 7 }\right) $ and $ \vec{v_2} = \left(8,~27\right) $ . | 1 |
6323 | Determine whether the vectors $ \vec{v_1} = \left(4,~4,~2\right) $, $ \vec{v_2} = \left(-8,~6,~1\right) $ and $ \vec{v_3} = \left(-8,~-2,~1\right)$ are linearly independent or dependent. | 1 |
6324 | Find the sum of the vectors $ \vec{v_1} = \left(5,~9\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 1 |
6325 | Find the angle between vectors $ \left(0,~-1,~-9\right)$ and $\left(7,~9,~-7\right)$. | 1 |
6326 | Find the angle between vectors $ \left(3,~2,~0\right)$ and $\left(1,~1,~-\sqrt{ 11 }\right)$. | 1 |
6327 | Find the angle between vectors $ \left(7,~1,~0\right)$ and $\left(1,~6,~7\right)$. | 1 |
6328 | Find the angle between vectors $ \left(7,~-5\right)$ and $\left(4,~1\right)$. | 1 |
6329 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-1\right) $ . | 1 |
6330 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2\right) $ . | 1 |
6331 | Find the angle between vectors $ \left(-8,~7,~8\right)$ and $\left(4,~-6,~1\right)$. | 1 |
6332 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~-2\right) $ . | 1 |
6333 | Determine whether the vectors $ \vec{v_1} = \left(0,~-1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent. | 1 |
6334 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~-5\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 1 |
6335 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~1,~0\right) $ and $ \vec{v_2} = \left(0,~-1,~1\right) $ . | 1 |
6336 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 1 |
6337 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~2\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
6338 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-5\right) $ . | 1 |
6339 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(-1,~4,~2\right) $ . | 1 |
6340 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~-3\right) $ . | 1 |
6341 | Find the sum of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(5,~6\right) $ . | 1 |
6342 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 1 |
6343 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~8\right) $ . | 1 |
6344 | Find the angle between vectors $ \left(3,~8\right)$ and $\left(7,~-8\right)$. | 1 |
6345 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~5\right) $ . | 1 |
6346 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~-5\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
6347 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 361 }{ 100 },~\dfrac{ 129 }{ 25 },~-\dfrac{ 233 }{ 100 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 379 }{ 100 },~0,~-\dfrac{ 561 }{ 100 }\right) $ . | 1 |
6348 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(0,~1,~4\right) $ . | 1 |
6349 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~4\right) $ . | 1 |
6350 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~7\right) $ . | 1 |