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
1901	Determine whether the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(2,~4\right) $ are linearly independent or dependent.	2
1902	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ .	2
1903	Find the angle between vectors $ \left(4,~2\right)$ and $\left(-2,~4\right)$.	2
1904	Find the difference of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(-3,~-8\right) $ .	2
1905	Find the angle between vectors $ \left(-2,~5\right)$ and $\left(6,~2\right)$.	2
1906	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(9,~-4,~6\right) $ .	2
1907	Find the sum of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(3,~1\right) $ .	2
1908	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~0\right) $ and $ \vec{v_2} = \left(2,~0,~-1\right) $ .	2
1909	Find the angle between vectors $ \left(-4,~3\right)$ and $\left(5,~12\right)$.	2
1910	Find the projection of the vector $ \vec{v_1} = \left(5,~12\right) $ on the vector $ \vec{v_2} = \left(-4,~3\right) $.	2
1911	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~0\right) $ .	2
1912	Find the projection of the vector $ \vec{v_1} = \left(2,~5\right) $ on the vector $ \vec{v_2} = \left(-2,~1\right) $.	2
1913	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~4\right) $ .	2
1914	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~4\right) $ .	2
1915	Find the sum of the vectors $ \vec{v_1} = \left(14,~-10\right) $ and $ \vec{v_2} = \left(9,~-4\right) $ .	2
1916	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~-1\right) $ .	2
1917	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-6,~6\right) $ .	2
1918	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~2\right) $ .	2
1919	Find the difference of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(4,~7\right) $ .	2
1920	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~2 \sqrt{ 3 }\right) $ .	2
1921	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~0,~3\right) $ and $ \vec{v_2} = \left(-2,~3,~6\right) $ .	2
1922	Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~3\right) $ and $ \vec{v_2} = \left(-2,~3,~6\right) $ .	2
1923	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(2,~1\right) $ .	2
1924	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(3,~2\right) $ .	2
1925	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 83 }{ 5 },~\dfrac{ 147 }{ 10 }\right) $ .	2
1926	Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-3\right) $ and $ \vec{v_2} = \left(-9,~-8\right) $ .	2
1927	Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~-8\right) $ and $ \vec{v_2} = \left(-6,~-3\right) $ .	2
1928	Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~8\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ .	2
1929	Find the angle between vectors $ \left(-9,~1\right)$ and $\left(8,~5\right)$.	2
1930	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~1\right) $ .	2
1931	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~2\right) $ .	2
1932	Find the angle between vectors $ \left(2,~2\right)$ and $\left(4,~-5\right)$.	2
1933	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ .	2
1934	Determine whether the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ are linearly independent or dependent.	2
1935	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~3\right) $ .	2
1936	Find the sum of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ .	2
1937	Calculate the cross product of the vectors $ \vec{v_1} = \left(-15,~0,~20\right) $ and $ \vec{v_2} = \left(0,~50,~0\right) $ .	2
1938	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~5\right) $ .	2
1939	Find the difference of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-3,~-7\right) $ .	2
1940	Find the angle between vectors $ \left(7,~4\right)$ and $\left(7,~4\right)$.	2
1941	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(5,~5\right) $ .	2
1942	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~3\right) $ .	2
1943	Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~3\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ .	2
1944	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-6,~3\right) $ .	2
1945	Find the difference of the vectors $ \vec{v_1} = \left(-6,~3\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ .	2
1946	Find the sum of the vectors $ \vec{v_1} = \left(-6,~3\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ .	2
1947	Find the sum of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~3\right) $ .	2
1948	Find the difference of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ .	2
1949	Find the sum of the vectors $ \vec{v_1} = \left(-5,~1\right) $ and $ \vec{v_2} = \left(-8,~6\right) $ .	2
1950	Find the difference of the vectors $ \vec{v_1} = \left(-5,~1\right) $ and $ \vec{v_2} = \left(-8,~6\right) $ .	2