Vectors

(the database of solved problems)

All the problems and solutions shown below were generated using the Vectors Calculator.

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ID	Problem	Count
1801	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-11,~5\right) $ .	2
1802	Find the angle between vectors $ \left(2,~-1.5,~-0.5\right)$ and $\left(0,~1,~0\right)$.	2
1803	Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ .	2
1804	Find the projection of the vector $ \vec{v_1} = \left(1,~-1\right) $ on the vector $ \vec{v_2} = \left(-3,~-2\right) $.	2
1805	Find the angle between vectors $ \left(2,~3\right)$ and $\left(-1,~-2\right)$.	2
1806	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(34,~16\right) $ .	2
1807	Find the sum of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ .	2
1808	Find the difference of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ .	2
1809	Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-1,~9\right) $ .	2
1810	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-3\right) $ .	2
1811	Find the angle between vectors $ \left(3,~1\right)$ and $\left(-3,~3\right)$.	2
1812	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~-1\right) $ .	2
1813	Determine whether the vectors $ \vec{v_1} = \left(0,~0,~0\right) $, $ \vec{v_2} = \left(0,~0,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent.	2
1814	Find the angle between vectors $ \left(2,~1,~-1\right)$ and $\left(-1,~-2,~5\right)$.	2
1815	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~3,~-1\right) $ .	2
1816	Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~-2\right) $ and $ \vec{v_2} = \left(4,~1,~1\right) $ .	2
1817	Find the difference of the vectors $ \vec{v_1} = \left(10,~8\right) $ and $ \vec{v_2} = \left(-4,~10\right) $ .	2
1818	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~3\right) $ .	2
1819	Find the angle between vectors $ \left(6,~-5,~-3\right)$ and $\left(4,~2,~2\right)$.	2
1820	Find the sum of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(9,~8\right) $ .	2
1821	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(5,~2\right) $ .	2
1822	Find the difference of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ .	2
1823	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~2\right) $ .	2
1824	Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~7\right) $ and $ \vec{v_2} = \left(-5,~-8\right) $ .	2
1825	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~-2\right) $ .	2
1826	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 13271 }{ 1000 },~-\dfrac{ 773789 }{ 10000 }\right) $ .	2
1827	Find the sum of the vectors $ \vec{v_1} = \left(5.2094,~29.5442\right) $ and $ \vec{v_2} = \left(-20,~-34.641\right) $ .	2
1828	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 55651 }{ 10000 },~\dfrac{ 5327 }{ 625 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 13 }{ 2 },~-11.2583\right) $ .	2
1829	Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ .	2
1830	Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-13,~-7\right) $ .	2
1831	Find the difference of the vectors $ \vec{v_1} = \left(5,~7\right) $ and $ \vec{v_2} = \left(7,~3\right) $ .	2
1832	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(12.6,~13.2\right) $ .	2
1833	Find the difference of the vectors $ \vec{v_1} = \left(12.6,~13.2\right) $ and $ \vec{v_2} = \left(4.73,~-4.99\right) $ .	2
1834	Find the angle between vectors $ \left(7,~2\right)$ and $\left(21,~6\right)$.	2
1835	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 41 }{ 10 },~\dfrac{ 9 }{ 10 }\right) $ .	2
1836	Find the difference of the vectors $ \vec{v_1} = \left(4,~-7\right) $ and $ \vec{v_2} = \left(2,~3\right) $ .	2
1837	Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ .	2
1838	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ .	2
1839	Find the difference of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ .	2
1840	Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(2,~3\right) $ .	2
1841	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-3\right) $ .	2
1842	Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~-2\right) $ and $ \vec{v_2} = \left(5,~0,~-5\right) $ .	2
1843	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(4,~4\right) $ .	2
1844	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~3\right) $ .	2
1845	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~6\right) $ .	2
1846	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~2\right) $ .	2
1847	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~6\right) $ .	2
1848	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~2\right) $ .	2
1849	Find the sum of the vectors $ \vec{v_1} = \left(-2,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ .	2
1850	Find the projection of the vector $ \vec{v_1} = \left(-2,~2\right) $ on the vector $ \vec{v_2} = \left(3,~4\right) $.	2