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
1851	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~-2\right) $ .	2
1852	Find the difference of the vectors $ \vec{v_1} = \left(12,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ .	2
1853	Find the projection of the vector $ \vec{v_1} = \left(-4,~3\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $.	2
1854	Find the sum of the vectors $ \vec{v_1} = \left(6,~7\right) $ and $ \vec{v_2} = \left(3,~4\right) $ .	2
1855	Find the angle between vectors $ \left(6,~7\right)$ and $\left(6,~-7\right)$.	2
1856	Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 4 },~\dfrac{ 147 }{ 50 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 281 }{ 100 },~\dfrac{ 53 }{ 100 }\right) $ .	2
1857	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~8\right) $ .	2
1858	Find the sum of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ .	2
1859	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~8\right) $ and $ \vec{v_2} = \left(9,~-2\right) $ .	2
1860	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~8\right) $ .	2
1861	Find the angle between vectors $ \left(89,~157\right)$ and $\left(237,~326\right)$.	2
1862	Find the difference of the vectors $ \vec{v_1} = \left(89,~157\right) $ and $ \vec{v_2} = \left(237,~326\right) $ .	2
1863	Find the sum of the vectors $ \vec{v_1} = \left(89,~157\right) $ and $ \vec{v_2} = \left(237,~326\right) $ .	2
1864	Calculate the dot product of the vectors $ \vec{v_1} = \left(89,~157\right) $ and $ \vec{v_2} = \left(237,~326\right) $ .	2
1865	Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~0,~2\right) $ and $ \vec{v_2} = \left(0,~3,~1\right) $ .	2
1866	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ .	2
1867	Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(-4,~12\right) $ .	2
1868	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ .	2
1869	Find the angle between vectors $ \left(-3,~1\right)$ and $\left(-9,~3\right)$.	2
1870	Find the angle between vectors $ \left(-\sqrt{ 3 },~-1\right)$ and $\left(2,~2 \sqrt{ 3 }\right)$.	2
1871	Find the angle between vectors $ \left(-3,~3\right)$ and $\left(9,~-9\right)$.	2
1872	Determine whether the vectors $ \vec{v_1} = \left(-1,~-2\right) $ and $ \vec{v_2} = \left(8,~-4\right) $ are linearly independent or dependent.	2
1873	Determine whether the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(-1,~-1\right) $ are linearly independent or dependent.	2
1874	Determine whether the vectors $ \vec{v_1} = \left(-6,~2\right) $ and $ \vec{v_2} = \left(-12,~36\right) $ are linearly independent or dependent.	2
1875	Determine whether the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(-12,~36\right) $ are linearly independent or dependent.	2
1876	Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(7,~0\right) $ .	2
1877	Find the difference of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(1,~0\right) $ .	2
1878	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~3,~2\right) $ .	2
1879	Find the angle between vectors $ \left(-3,~1,~2\right)$ and $\left(1,~0,~2\right)$.	2
1880	Find the sum of the vectors $ \vec{v_1} = \left(-4,~-5\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ .	2
1881	Find the difference of the vectors $ \vec{v_1} = \left(170,~0\right) $ and $ \vec{v_2} = \left(-85,~140\right) $ .	2
1882	Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~1\right) $ and $ \vec{v_2} = \left(3,~-4\right) $ .	2
1883	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 3 }{ 20 },~\dfrac{ 1 }{ 5 }\right) $ .	2
1884	Find the sum of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ .	2
1885	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(10,~0\right) $ .	2
1886	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~\sqrt{ 8 }\right) $ .	2
1887	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-6,~-1\right) $ .	2
1888	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~-8\right) $ .	2
1889	Find the difference of the vectors $ \vec{v_1} = \left(-4,~-3\right) $ and $ \vec{v_2} = \left(-1,~0\right) $ .	2
1890	Find the angle between vectors $ \left(\dfrac{ 3 }{ 4 },~2\right)$ and $\left(3,~-2\right)$.	2
1891	Find the sum of the vectors $ \vec{v_1} = \left(-2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 3 }{ 2 },~\dfrac{ 15 }{ 2 }\right) $ .	2
1892	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(1,~\dfrac{ 1 }{ 4 }\right) $ .	2
1893	Determine whether the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent.	2
1894	Find the difference of the vectors $ \vec{v_1} = \left(4,~-10\right) $ and $ \vec{v_2} = \left(-9,~-6\right) $ .	2
1895	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~1\right) $ .	2
1896	Find the sum of the vectors $ \vec{v_1} = \left(-8,~-5\right) $ and $ \vec{v_2} = \left(4,~9\right) $ .	2
1897	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(3,~5\right) $ .	2
1898	Calculate the dot product of the vectors $ \vec{v_1} = \left(-20,~-25\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ .	2
1899	Determine whether the vectors $ \vec{v_1} = \left(1,~-5,~0\right) $, $ \vec{v_2} = \left(2,~-4,~3\right) $ and $ \vec{v_3} = \left(0,~-3,~-2\right)$ are linearly independent or dependent.	2
1900	Find the sum of the vectors $ \vec{v_1} = \left(-20,~-25\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ .	2