Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1951 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~1\right) $ . | 2 |
1952 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(6,~-5\right) $ . | 2 |
1953 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~30\right) $ . | 2 |
1954 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~5\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 2 |
1955 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\sqrt{ 17 },~5\right) $ . | 2 |
1956 | Find the angle between vectors $ \left(-5,~2\right)$ and $\left(2,~1\right)$. | 2 |
1957 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(2,~2,~2\right) $ . | 2 |
1958 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 26 }{ 5 },~\dfrac{ 5 }{ 2 },~-\dfrac{ 9 }{ 2 }\right) $ . | 2 |
1959 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-3\right) $ . | 2 |
1960 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~0\right) $ . | 2 |
1961 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 2 |
1962 | Find the angle between vectors $ \left(3,~1\right)$ and $\left(-4,~-3\right)$. | 2 |
1963 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 2 |
1964 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-3\right) $ and $ \vec{v_2} = \left(-9,~-8\right) $ . | 2 |
1965 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~6\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 2 |
1966 | Find the angle between vectors $ \left(4,~1\right)$ and $\left(2,~5\right)$. | 2 |
1967 | Find the angle between vectors $ \left(4,~5\right)$ and $\left(6,~7\right)$. | 2 |
1968 | Find the angle between vectors $ \left(6,~11\right)$ and $\left(3,~4\right)$. | 2 |
1969 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 12 }{ 25 },~\dfrac{ 13 }{ 25 }\right) $ . | 2 |
1970 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-4,~0\right) $ and $ \vec{v_2} = \left(0,~0,~\dfrac{ 1 }{ 10 }\right) $ . | 2 |
1971 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-9\right) $ and $ \vec{v_2} = \left(-3,~1\right) $ . | 2 |
1972 | Find the angle between vectors $ \left(-2,~2\right)$ and $\left(2,~1\right)$. | 2 |
1973 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-1,~9\right) $ . | 2 |
1974 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~-8\right) $ and $ \vec{v_2} = \left(-6,~-3\right) $ . | 2 |
1975 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0.2103,~0.7071,~0.6751\right) $ . | 2 |
1976 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 2 |
1977 | Find the difference of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-2,~8\right) $ . | 2 |
1978 | Find the magnitude of the vector $ \| \vec{v} \| = \left(15,~83\right) $ . | 2 |
1979 | Find the angle between vectors $ \left(5,~2\right)$ and $\left(-5,~2\right)$. | 2 |
1980 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~1\right) $ and $ \vec{v_2} = \left(1,~6\right) $ . | 2 |
1981 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(5,~-7\right) $ . | 2 |
1982 | Find the angle between vectors $ \left(4,~4\right)$ and $\left(8,~-2\right)$. | 2 |
1983 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 2 |
1984 | Find the angle between vectors $ \left(12,~35\right)$ and $\left(60,~-11\right)$. | 2 |
1985 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-3\right) $ . | 2 |
1986 | Find the angle between vectors $ \left(6,~-3\right)$ and $\left(-2,~8\right)$. | 2 |
1987 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-3\right) $ . | 2 |
1988 | Find the magnitude of the vector $ \| \vec{v} \| = \left(50,~57\right) $ . | 2 |
1989 | Find the angle between vectors $ \left(-7,~0\right)$ and $\left(8,~-1\right)$. | 2 |
1990 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0\right) $ . | 2 |
1991 | Determine whether the vectors $ \vec{v_1} = \left(5,~6\right) $ and $ \vec{v_2} = \left(10,~5\right) $ are linearly independent or dependent. | 2 |
1992 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 1 }{ 2 },~0\right) $ . | 2 |
1993 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~-4\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 2 |
1994 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~3\right) $ and $ \vec{v_2} = \left(0,~3,~1\right) $ . | 2 |
1995 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 4 },~2\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 2 |
1996 | Calculate the dot product of the vectors $ \vec{v_1} = \left(50,~57\right) $ and $ \vec{v_2} = \left(29,~1\right) $ . | 2 |
1997 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 2 |
1998 | Find the projection of the vector $ \vec{v_1} = \left(-7,~0\right) $ on the vector $ \vec{v_2} = \left(8,~-1\right) $. | 2 |
1999 | Find the projection of the vector $ \vec{v_1} = \left(1,~0\right) $ on the vector $ \vec{v_2} = \left(2,~1\right) $. | 2 |
2000 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~6\right) $ and $ \vec{v_2} = \left(10,~5\right) $ . | 2 |