Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1851 | Find the projection of the vector $ \vec{v_1} = \left(-4,~4\right) $ on the vector $ \vec{v_2} = \left(12,~16\right) $. | 2 |
1852 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 2 |
1853 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 2 |
1854 | Find the sum of the vectors $ \vec{v_1} = \left(-50,~90\right) $ and $ \vec{v_2} = \left(81,~-63\right) $ . | 2 |
1855 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 8 }{ 9 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right) $ . | 2 |
1856 | Find the angle between vectors $ \left(16,~-6\right)$ and $\left(3,~1\right)$. | 2 |
1857 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-4\right) $ and $ \vec{v_2} = \left(7,~1\right) $ . | 2 |
1858 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 2 |
1859 | Find the projection of the vector $ \vec{v_1} = \left(-2,~2\right) $ on the vector $ \vec{v_2} = \left(3,~4\right) $. | 2 |
1860 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-2\right) $ . | 2 |
1861 | Determine whether the vectors $ \vec{v_1} = \left(-5,~10\right) $ and $ \vec{v_2} = \left(-10,~20\right) $ are linearly independent or dependent. | 2 |
1862 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 9 },~\dfrac{ 8 }{ 9 }\right)$ and $\left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right)$. | 2 |
1863 | Find the difference of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(0,~8\right) $ . | 2 |
1864 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 9 }{ 41 },~\dfrac{ 40 }{ 41 }\right) $ . | 2 |
1865 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
1866 | Find the sum of the vectors $ \vec{v_1} = \left(50,~90\right) $ and $ \vec{v_2} = \left(81,~-63\right) $ . | 2 |
1867 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ . | 2 |
1868 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~1\right) $ and $ \vec{v_2} = \left(3,~-4\right) $ . | 2 |
1869 | Find the sum of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 2 |
1870 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1210,~0\right) $ . | 2 |
1871 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 3 }{ 4 }\right) $ . | 2 |
1872 | Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(10,~10\right) $ . | 2 |
1873 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1\right) $ . | 2 |
1874 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 2 |
1875 | Find the sum of the vectors $ \vec{v_1} = \left(1210,~0\right) $ and $ \vec{v_2} = \left(395.993,~1477.87\right) $ . | 2 |
1876 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~20\right) $ . | 2 |
1877 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 3 }{ 4 }\right) $ . | 2 |
1878 | Find the sum of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(10,~0\right) $ . | 2 |
1879 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 2 |
1880 | Determine whether the vectors $ \vec{v_1} = \left(-6,~4\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ are linearly independent or dependent. | 2 |
1881 | Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~1\right) $ and $ \vec{v_2} = \left(1,~10\right) $ . | 2 |
1882 | Find the difference of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 2 |
1883 | Find the projection of the vector $ \vec{v_1} = \left(6,~9\right) $ on the vector $ \vec{v_2} = \left(3,~-2\right) $. | 2 |
1884 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 3 }{ 4 }\right) $ . | 2 |
1885 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 2 |
1886 | Determine whether the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(8,~-6\right) $ are linearly independent or dependent. | 2 |
1887 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-1\right) $ . | 2 |
1888 | Find the difference of the vectors $ \vec{v_1} = \left(-18,~18\right) $ and $ \vec{v_2} = \left(4,~25\right) $ . | 2 |
1889 | Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~1\right) $ and $ \vec{v_2} = \left(10,~1\right) $ . | 2 |
1890 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $ and $ \vec{v_2} = \left(4,~-5,~6\right) $ . | 2 |
1891 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0.1667,~0.125\right) $ and $ \vec{v_2} = \left(0.8333,~0.875\right) $ . | 2 |
1892 | Find the sum of the vectors $ \vec{v_1} = \left(3,~0\right) $ and $ \vec{v_2} = \left(0,~6\right) $ . | 2 |
1893 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 3 }{ 4 }\right) $ are linearly independent or dependent. | 2 |
1894 | Find the difference of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 2 |
1895 | Find the angle between vectors $ \left(-4,~3\right)$ and $\left(8,~-6\right)$. | 2 |
1896 | Find the difference of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 2 |
1897 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(3,~3\right) $ . | 2 |
1898 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-4,~1\right) $ . | 2 |
1899 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~7\right) $ . | 2 |
1900 | Find the projection of the vector $ \vec{v_1} = \left(4,~1\right) $ on the vector $ \vec{v_2} = \left(2,~5\right) $. | 2 |