Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4851 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 5 }{ 2 },~6\right) $ and $ \vec{v_2} = \left(-10,~24\right) $ . | 1 |
| 4852 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
| 4853 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(3,~-5\right) $ . | 1 |
| 4854 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 1 |
| 4855 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-5\right) $ and $ \vec{v_2} = \left(0,~6\right) $ . | 1 |
| 4856 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 6 }{ 5 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right) $ . | 1 |
| 4857 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right) $ . | 1 |
| 4858 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 63 }{ 10 },~8\right) $ . | 1 |
| 4859 | Find the sum of the vectors $ \vec{v_1} = \left(8,~-4\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
| 4860 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~0,~3\right) $ and $ \vec{v_2} = \left(20,~-15,~35\right) $ . | 1 |
| 4861 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~0,~-3\right) $ and $ \vec{v_2} = \left(20,~-15,~35\right) $ . | 1 |
| 4862 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-21,~15,~-38\right) $ . | 1 |
| 4863 | Find the angle between vectors $ \left(0,~-1\right)$ and $\left(1,~-2\right)$. | 1 |
| 4864 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~2\right) $ and $ \vec{v_2} = \left(-3,~-3\right) $ . | 1 |
| 4865 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(-3,~-3\right) $ . | 1 |
| 4866 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 1 |
| 4867 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~8\right) $ . | 1 |
| 4868 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~4\right) $ . | 1 |
| 4869 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-4,~5\right) $ and $ \vec{v_2} = \left(-4,~5,~-5\right) $ . | 1 |
| 4870 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~4,~-1\right) $ and $ \vec{v_2} = \left(3,~4,~4\right) $ . | 1 |
| 4871 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-9,~9,~-10\right) $ and $ \vec{v_2} = \left(4,~-9,~2\right) $ . | 1 |
| 4872 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1107.1,~-116.86,~7.92\right) $ . | 1 |
| 4873 | Find the difference of the vectors $ \vec{v_1} = \left(1107.1,~-116.86,~7.92\right) $ and $ \vec{v_2} = \left(1122.1199,~-132.0958,~-15.5302\right) $ . | 1 |
| 4874 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-18,~-1\right) $ and $ \vec{v_2} = \left(4,~-12,~0\right) $ . | 1 |
| 4875 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~-2,~-7\right) $ and $ \vec{v_2} = \left(-5,~-2,~8\right) $ . | 1 |
| 4876 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~-2,~-7\right) $ and $ \vec{v_2} = \left(-7,~-2,~8\right) $ . | 1 |
| 4877 | Find the difference of the vectors $ \vec{v_1} = \left(1134.4033,~-87.2012,~-46.3562\right) $ and $ \vec{v_2} = \left(1118.78,~-90.07,~-18.16\right) $ . | 1 |
| 4878 | Find the projection of the vector $ \vec{v_1} = \left(-\dfrac{ 156233 }{ 10000 },~\dfrac{ 1793 }{ 625 },~-\dfrac{ 140981 }{ 5000 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 1 }{ 5 },~-1\right) $. | 1 |
| 4879 | Find the projection of the vector $ \vec{v_1} = \left(-\dfrac{ 156233 }{ 10000 },~\dfrac{ 1793 }{ 625 },~-\dfrac{ 140981 }{ 5000 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 1 }{ 10 },~-1\right) $. | 1 |
| 4880 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(5,~0\right) $ . | 1 |
| 4881 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~-2\right) $ and $ \vec{v_2} = \left(-1,~0,~0\right) $ . | 1 |
| 4882 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~0,~-2\right) $ and $ \vec{v_2} = \left(-1,~0,~-1\right) $ . | 1 |
| 4883 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-1\right) $ . | 1 |
| 4884 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 1 |
| 4885 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 1 |
| 4886 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~5\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ . | 1 |
| 4887 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ . | 1 |
| 4888 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 1 |
| 4889 | Find the sum of the vectors $ \vec{v_1} = \left(-11,~-4\right) $ and $ \vec{v_2} = \left(8,~7\right) $ . | 1 |
| 4890 | Find the difference of the vectors $ \vec{v_1} = \left(-7,~-5\right) $ and $ \vec{v_2} = \left(-2,~-3\right) $ . | 1 |
| 4891 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ . | 1 |
| 4892 | Find the sum of the vectors $ \vec{v_1} = \left(1,~5\right) $ and $ \vec{v_2} = \left(-3,~9\right) $ . | 1 |
| 4893 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(2,~9\right) $ . | 1 |
| 4894 | Determine whether the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(4,~11\right) $ are linearly independent or dependent. | 1 |
| 4895 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~9\right) $ . | 1 |
| 4896 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0\right) $ . | 1 |
| 4897 | Find the angle between vectors $ \left(5,~0\right)$ and $\left(-1,~5\right)$. | 1 |
| 4898 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-5,~-4\right) $ and $ \vec{v_2} = \left(3,~-2,~-1\right) $ . | 1 |
| 4899 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-5,~-4\right) $ and $ \vec{v_2} = \left(0,~-4,~-3\right) $ . | 1 |
| 4900 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~0\right) $ and $ \vec{v_2} = \left(2,~-1,~1\right) $ . | 1 |
