Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5901 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-2,~-1\right) $ and $ \vec{v_2} = \left(7,~-3,~-4\right) $ . | 1 |
| 5902 | Find the angle between vectors $ \left(13.24,~7.04\right)$ and $\left(10,~17.32\right)$. | 1 |
| 5903 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4,~0\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
| 5904 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4,~0\right) $ and $ \vec{v_2} = \left(3,~4,~0\right) $ . | 1 |
| 5905 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~4,~-3\right) $ and $ \vec{v_2} = \left(0,~3,~-5\right) $ . | 1 |
| 5906 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-11,~5,~3\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
| 5907 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~4,~-3\right) $ . | 1 |
| 5908 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~4,~-3\right) $ . | 1 |
| 5909 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~3,~3\right) $ and $ \vec{v_2} = \left(0,~3,~-5\right) $ . | 1 |
| 5910 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~3,~3\right) $ and $ \vec{v_2} = \left(0,~3,~-5\right) $ . | 1 |
| 5911 | Find the angle between vectors $ \left(-10.07,~14.92\right)$ and $\left(-15.73,~19.43\right)$. | 1 |
| 5912 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~1\right) $ and $ \vec{v_2} = \left(1,~1,~5\right) $ . | 1 |
| 5913 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~1\right) $ and $ \vec{v_2} = \left(1,~1,~5\right) $ . | 1 |
| 5914 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-19,~4\right) $ and $ \vec{v_2} = \left(3,~1,~0\right) $ . | 1 |
| 5915 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-19,~4\right) $ and $ \vec{v_2} = \left(3,~1,~0\right) $ . | 1 |
| 5916 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~-2\right) $ . | 1 |
| 5917 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~1\right) $ and $ \vec{v_2} = \left(2,~-2,~2\right) $ . | 1 |
| 5918 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~1\right) $ and $ \vec{v_2} = \left(4,~-2,~1\right) $ . | 1 |
| 5919 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 5920 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(2,~2,~2\right) $ . | 1 |
| 5921 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-1\right) $ . | 1 |
| 5922 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
| 5923 | Find the angle between vectors $ \left(0.2103,~0.7071,~0.6751\right)$ and $\left(-0.2102,~0.7071,~-0.6751\right)$. | 1 |
| 5924 | Determine whether the vectors $ \vec{v_1} = \left(0.2103,~0.7071,~0.6751\right) $, $ \vec{v_2} = \left(-0.2102,~0.7071,~-0.6751\right) $ and $ \vec{v_3} = \left(-0.9548,~0,~0.2974\right)$ are linearly independent or dependent. | 1 |
| 5925 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~8\right) $ . | 1 |
| 5926 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~8\right) $ and $ \vec{v_2} = \left(4,~-7\right) $ . | 1 |
| 5927 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-1,~0\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
| 5928 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~5\right) $, $ \vec{v_2} = \left(2,~-2,~5\right) $ and $ \vec{v_3} = \left(-3,~3,~5\right)$ are linearly independent or dependent. | 1 |
| 5929 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~9\right) $ . | 1 |
| 5930 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 1 |
| 5931 | Determine whether the vectors $ \vec{v_1} = \left(7,~-6\right) $ and $ \vec{v_2} = \left(4,~1\right) $ are linearly independent or dependent. | 1 |
| 5932 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 5933 | Find the projection of the vector $ \vec{v_1} = \left(-5,~1,~10\right) $ on the vector $ \vec{v_2} = \left(-3,~-1,~2\right) $. | 1 |
| 5934 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-2\right) $ . | 1 |
| 5935 | Find the projection of the vector $ \vec{v_1} = \left(-4,~-2\right) $ on the vector $ \vec{v_2} = \left(1,~-7\right) $. | 1 |
| 5936 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~1,~10\right) $ and $ \vec{v_2} = \left(-3,~-1,~2\right) $ . | 1 |
| 5937 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~1,~10\right) $ . | 1 |
| 5938 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-1,~2\right) $ and $ \vec{v_2} = \left(-3,~-1,~2\right) $ . | 1 |
| 5939 | Find the projection of the vector $ \vec{v_1} = \left(-4,~-7,~-2\right) $ on the vector $ \vec{v_2} = \left(-2,~-3,~1\right) $. | 1 |
| 5940 | 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 |
| 5941 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~1\right) $ . | 1 |
| 5942 | Find the projection of the vector $ \vec{v_1} = \left(3,~1,~-1\right) $ on the vector $ \vec{v_2} = \left(-1,~-10,~8\right) $. | 1 |
| 5943 | Find the projection of the vector $ \vec{v_1} = \left(-1,~-10,~8\right) $ on the vector $ \vec{v_2} = \left(3,~1,~-1\right) $. | 1 |
| 5944 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-10,~13\right) $ . | 1 |
| 5945 | Find the projection of the vector $ \vec{v_1} = \left(2,~-9,~9\right) $ on the vector $ \vec{v_2} = \left(2,~2,~-1\right) $. | 1 |
| 5946 | Find the projection of the vector $ \vec{v_1} = \left(-3,~-1,~-2\right) $ on the vector $ \vec{v_2} = \left(10,~-2,~-10\right) $. | 1 |
| 5947 | Find the projection of the vector $ \vec{v_1} = \left(10,~-2,~-10\right) $ on the vector $ \vec{v_2} = \left(-3,~-1,~-2\right) $. | 1 |
| 5948 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~9,~4\right) $ and $ \vec{v_2} = \left(6,~-2,~8\right) $ . | 1 |
| 5949 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~9,~4\right) $ and $ \vec{v_2} = \left(6,~-2,~8\right) $ . | 1 |
| 5950 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~6,~9\right) $ and $ \vec{v_2} = \left(3,~-7,~4\right) $ . | 1 |
