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
1951	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~7\right) $ .	2
1952	Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-8,~4\right) $ .	2
1953	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~3\right) $ and $ \vec{v_2} = \left(7,~1\right) $ .	2
1954	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ .	2
1955	Find the angle between vectors $ \left(3,~4\right)$ and $\left(2,~-1\right)$.	2
1956	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(13,~5\right) $ .	2
1957	Find the projection of the vector $ \vec{v_1} = \left(5,~2,~5\right) $ on the vector $ \vec{v_2} = \left(2,~-1,~2\right) $.	2
1958	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~6\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ .	2
1959	Find the angle between vectors $ \left(\dfrac{ 7361 }{ 50 },~-85\right)$ and $\left(\dfrac{ 2121 }{ 100 },~\dfrac{ 2121 }{ 100 }\right)$.	2
1960	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~-2\right) $ .	2
1961	Calculate the dot product of the vectors $ \vec{v_1} = \left(13,~0\right) $ and $ \vec{v_2} = \left(0,~-5\right) $ .	2
1962	Find the sum of the vectors $ \vec{v_1} = \left(13,~0\right) $ and $ \vec{v_2} = \left(0,~-5\right) $ .	2
1963	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(13,~-5\right) $ .	2
1964	Find the angle between vectors $ \left(13,~0\right)$ and $\left(0,~-5\right)$.	2
1965	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~3\right) $ .	2
1966	Find the angle between vectors $ \left(1,~3\right)$ and $\left(3,~-4\right)$.	2
1967	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~1\right) $ .	2
1968	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ .	2
1969	Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(4,~7\right) $ .	2
1970	Find the difference of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(11,~-4\right) $ .	2
1971	Find the angle between vectors $ \left(-1,~2\right)$ and $\left(1,~1\right)$.	2
1972	Find the angle between vectors $ \left(0,~0,~45\right)$ and $\left(\dfrac{ 95373 }{ 10000 },~0,~\dfrac{ 95373 }{ 10000 }\right)$.	2
1973	Find the projection of the vector $ \vec{v_1} = \left(6,~1\right) $ on the vector $ \vec{v_2} = \left(5,~0\right) $.	2
1974	Find the difference of the vectors $ \vec{v_1} = \left(8,~0\right) $ and $ \vec{v_2} = \left(-20,~-16\right) $ .	2
1975	Find the difference of the vectors $ \vec{v_1} = \left(-24,~21\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ .	2
1976	Find the projection of the vector $ \vec{v_1} = \left(-2,~0\right) $ on the vector $ \vec{v_2} = \left(3,~0\right) $.	2
1977	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
1978	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	2
1979	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~0\right) $ .	2
1980	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ .	2
1981	Find the angle between vectors $ \left(2,~-6\right)$ and $\left(6,~2\right)$.	2
1982	Find the angle between vectors $ \left(2,~-2\right)$ and $\left(4,~2\right)$.	2
1983	Find the angle between vectors $ \left(2,~-5\right)$ and $\left(4,~2\right)$.	2
1984	Find the angle between vectors $ \left(3,~-1\right)$ and $\left(3,~1\right)$.	2
1985	Find the angle between vectors $ \left(4,~4\right)$ and $\left(-4,~4\right)$.	2
1986	Find the angle between vectors $ \left(3,~22\right)$ and $\left(7,~-3\right)$.	2
1987	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
1988	Find the angle between vectors $ \left(1,~1\right)$ and $\left(1,~1\right)$.	2
1989	Find the angle between vectors $ \left(1,~1\right)$ and $\left(1,~-1\right)$.	2
1990	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(12,~15\right) $ .	2
1991	Find the sum of the vectors $ \vec{v_1} = \left(8,~4\right) $ and $ \vec{v_2} = \left(-9,~15\right) $ .	2
1992	Find the sum of the vectors $ \vec{v_1} = \left(-12,~-6\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ .	2
1993	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~5\right) $ .	2
1994	Find the angle between vectors $ \left(2,~5\right)$ and $\left(1,~2\right)$.	2
1995	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(1,~2\right) $ .	2
1996	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(32,~8\right) $ .	2
1997	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-3,~0\right) $ .	2
1998	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~-2\right) $ .	2
1999	Find the projection of the vector $ \vec{v_1} = \left(4,~-4\right) $ on the vector $ \vec{v_2} = \left(6,~-6\right) $.	2
2000	Find the angle between vectors $ \left(4,~-4\right)$ and $\left(6,~-6\right)$.	2