Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1801 | Find the sum of the vectors $ \vec{v_1} = \left(10,~-9\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ . | 2 |
1802 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ . | 2 |
1803 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-8\right) $ . | 2 |
1804 | Find the angle between vectors $ \left(-7,~7\right)$ and $\left(6,~-4\right)$. | 2 |
1805 | Find the angle between vectors $ \left(-9,~7\right)$ and $\left(7,~5\right)$. | 2 |
1806 | Calculate the dot product of the vectors $ \vec{v_1} = \left(25,~20\right) $ and $ \vec{v_2} = \left(6,~-6\right) $ . | 2 |
1807 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-3\right) $ . | 2 |
1808 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~8\right) $ . | 2 |
1809 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(3,~-4\right) $ . | 2 |
1810 | Find the angle between vectors $ \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right)$ and $\left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right)$. | 2 |
1811 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(5,~7\right) $ . | 2 |
1812 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 2 |
1813 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-34.47,~-28.93\right) $ and $ \vec{v_2} = \left(0,~0.42,~0.91\right) $ . | 2 |
1814 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~0,~2\right) $ . | 2 |
1815 | Determine whether the vectors $ \vec{v_1} = \left(-9,~7\right) $ and $ \vec{v_2} = \left(7,~5\right) $ are linearly independent or dependent. | 2 |
1816 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~-2\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ . | 2 |
1817 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 2 },~\dfrac{ 2 }{ 7 }\right) $ and $ \vec{v_2} = \left(6,~23\right) $ . | 2 |
1818 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-12,~-16\right) $ . | 2 |
1819 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 2 |
1820 | Find the difference of the vectors $ \vec{v_1} = \left(220,~280\right) $ and $ \vec{v_2} = \left(-150,~283.1\right) $ . | 2 |
1821 | Find the difference of the vectors $ \vec{v_1} = \left(-36,~4\right) $ and $ \vec{v_2} = \left(21,~13\right) $ . | 2 |
1822 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ are linearly independent or dependent. | 2 |
1823 | Find the angle between vectors $ \left(-1,~1\right)$ and $\left(3,~-3\right)$. | 2 |
1824 | Find the sum 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 |
1825 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3090,~-2954\right) $ . | 2 |
1826 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
1827 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(12,~16\right) $ . | 2 |
1828 | Find the angle between vectors $ \left(2,~-6\right)$ and $\left(6,~2\right)$. | 2 |
1829 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 2 |
1830 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(-2,~1,~1\right) $ . | 2 |
1831 | Find the difference of the vectors $ \vec{v_1} = \left(48,~-16\right) $ and $ \vec{v_2} = \left(27,~-8\right) $ . | 2 |
1832 | Calculate the dot product 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 |
1833 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~17\right) $ . | 2 |
1834 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 17043 }{ 10 },~\dfrac{ 31 }{ 5 },~-\dfrac{ 5772 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8611 }{ 5 },~\dfrac{ 13 }{ 2 },~-\dfrac{ 5748 }{ 5 }\right) $ . | 2 |
1835 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(12,~16\right) $ . | 2 |
1836 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~5\right) $ . | 2 |
1837 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~5\right) $ and $ \vec{v_2} = \left(6,~3\right) $ . | 2 |
1838 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 7 },~\dfrac{ 2 }{ 7 }\right) $ and $ \vec{v_2} = \left(6,~23\right) $ . | 2 |
1839 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~-2\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 2 |
1840 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 10 },~\dfrac{ 7 }{ 10 }\right) $ . | 2 |
1841 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(6,~2\right) $ . | 2 |
1842 | Find the sum of the vectors $ \vec{v_1} = \left(-20,~36\right) $ and $ \vec{v_2} = \left(63,~-49\right) $ . | 2 |
1843 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ . | 2 |
1844 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2\right) $ . | 2 |
1845 | Find the angle between vectors $ \left(-96,~-57,~-28\right)$ and $\left(-2,~0,~7\right)$. | 2 |
1846 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1,~-5\right) $ and $ \vec{v_2} = \left(6,~-\dfrac{ 3 }{ 2 },~-\dfrac{ 15 }{ 2 }\right) $ . | 2 |
1847 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-9\right) $ and $ \vec{v_2} = \left(8,~4\right) $ . | 2 |
1848 | Determine whether 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) $ are linearly independent or dependent. | 2 |
1849 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~-12\right) $ and $ \vec{v_2} = \left(4,~9\right) $ . | 2 |
1850 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-2,~2\right) $ . | 2 |