Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5401 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~4 \sqrt{ 3 }\right) $ . | 1 |
5402 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 5 }{ 2 },~\dfrac{ 5 }{ 2 },~1\right) $ and $ \vec{v_2} = \left(4,~6,~-9\right) $ . | 1 |
5403 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~-1,~2\right) $ . | 1 |
5404 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~-2,~-3\right) $ . | 1 |
5405 | Determine whether the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent. | 1 |
5406 | Find the angle between vectors $ \left(1,~2,~4\right)$ and $\left(3,~-2,~1\right)$. | 1 |
5407 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-1\right) $ . | 1 |
5408 | Find the angle between vectors $ \left(2,~6\right)$ and $\left(-6,~2\right)$. | 1 |
5409 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(-5,~-9,~8\right) $ . | 1 |
5410 | Find the angle between vectors $ \left(3,~2,~-5\right)$ and $\left(12,~8,~-20\right)$. | 1 |
5411 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-5\right) $ . | 1 |
5412 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~5,~-2\right) $ and $ \vec{v_2} = \left(80,~40,~-30\right) $ . | 1 |
5413 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~6\right) $ and $ \vec{v_2} = \left(-3,~-9\right) $ . | 1 |
5414 | Find the difference of the vectors $ \vec{v_1} = \left(1,~3,~5\right) $ and $ \vec{v_2} = \left(-2,~-6,~1\right) $ . | 1 |
5415 | Find the angle between vectors $ \left(7,~-6\right)$ and $\left(2,~-9\right)$. | 1 |
5416 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(16,~-18\right) $ . | 1 |
5417 | Find the difference of the vectors $ \vec{v_1} = \left(-25,~45\right) $ and $ \vec{v_2} = \left(18,~-14\right) $ . | 1 |
5418 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~4,~2\right) $ and $ \vec{v_2} = \left(0,~4,~4\right) $ . | 1 |
5419 | Find the angle between vectors $ \left(5,~17\right)$ and $\left(3,~-1\right)$. | 1 |
5420 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~1\right) $ . | 1 |
5421 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(4,~5\right)$. | 1 |
5422 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
5423 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-6,~10\right) $ and $ \vec{v_2} = \left(1,~-3,~-5\right) $ . | 1 |
5424 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~7\right) $ . | 1 |
5425 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~15\right) $ . | 1 |
5426 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-6,~-10,~-5\right) $ and $ \vec{v_2} = \left(-1,~-17,~-2\right) $ . | 1 |
5427 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~0,~0\right) $ . | 1 |
5428 | Find the angle between vectors $ \left(-4,~1,~1\right)$ and $\left(1,~19,~0\right)$. | 1 |
5429 | Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~-4\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 1 |
5430 | Find the angle between vectors $ \left(1,~2,~-3\right)$ and $\left(4,~-5,~6\right)$. | 1 |
5431 | Find the projection of the vector $ \vec{v_1} = \left(-7,~-3\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 1 |
5432 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-6\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 1 |
5433 | Find the difference of the vectors $ \vec{v_1} = \left(4,~10,~16\right) $ and $ \vec{v_2} = \left(-2,~-6,~1\right) $ . | 1 |
5434 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-2\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ . | 1 |
5435 | Find the projection of the vector $ \vec{v_1} = \left(4,~-5\right) $ on the vector $ \vec{v_2} = \left(1,~9\right) $. | 1 |
5436 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-4,~2\right) $ and $ \vec{v_2} = \left(-1,~-2,~2\right) $ . | 1 |
5437 | Find the angle between vectors $ \left(4,~4 \sqrt{ 3 }\right)$ and $\left(1,~0\right)$. | 1 |
5438 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~-1\right) $ and $ \vec{v_2} = \left(1,~3,~-5\right) $ . | 1 |
5439 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~5\right) $ . | 1 |
5440 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-10,~-5\right) $ and $ \vec{v_2} = \left(-1,~-17,~-2\right) $ . | 1 |
5441 | Find the angle between vectors $ \left(2,~-2\right)$ and $\left(2,~2\right)$. | 1 |
5442 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~1\right) $ . | 1 |
5443 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~2\right) $ and $ \vec{v_2} = \left(8,~2\right) $ . | 1 |
5444 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~9,~4\right) $ and $ \vec{v_2} = \left(6,~16,~15\right) $ . | 1 |
5445 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 1 }{ 9 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 8 }{ 9 }\right) $ . | 1 |
5446 | Determine whether the vectors $ \vec{v_1} = \left(8,~20\right) $ and $ \vec{v_2} = \left(-2,~-5\right) $ are linearly independent or dependent. | 1 |
5447 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-1\right) $ and $ \vec{v_2} = \left(1,~-1,~1\right) $ . | 1 |
5448 | | 1 |
5449 | Find the projection of the vector $ \vec{v_1} = \left(-1,~5\right) $ on the vector $ \vec{v_2} = \left(-5,~5\right) $. | 1 |
5450 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-5,~-4\right) $ and $ \vec{v_2} = \left(6,~-6,~-4\right) $ . | 1 |