Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2001 | Find the sum of the vectors $ \vec{v_1} = \left(50,~57\right) $ and $ \vec{v_2} = \left(29,~1\right) $ . | 2 |
2002 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 2 |
2003 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-6,~3\right) $ . | 2 |
2004 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~0\right) $ . | 2 |
2005 | Find the projection of the vector $ \vec{v_1} = \left(2,~0\right) $ on the vector $ \vec{v_2} = \left(2,~1\right) $. | 2 |
2006 | Find the projection of the vector $ \vec{v_1} = \left(6,~-3\right) $ on the vector $ \vec{v_2} = \left(-2,~8\right) $. | 2 |
2007 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 2 |
2008 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~5\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 2 |
2009 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-13,~9\right) $ and $ \vec{v_2} = \left(14,~-6\right) $ . | 2 |
2010 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 2 |
2011 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~3\right) $ and $ \vec{v_2} = \left(0,~3,~-1\right) $ . | 2 |
2012 | Find the projection of the vector $ \vec{v_1} = \left(2,~0\right) $ on the vector $ \vec{v_2} = \left(4,~2\right) $. | 2 |
2013 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 2 |
2014 | Find the angle between vectors $ \left(0,~-1\right)$ and $\left(4,~1\right)$. | 2 |
2015 | Find the sum of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 2 |
2016 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-1\right) $ . | 2 |
2017 | Find the angle between vectors $ \left(-5,~9\right)$ and $\left(7,~-1\right)$. | 2 |
2018 | Determine whether the vectors $ \vec{v_1} = \left(50,~57\right) $ and $ \vec{v_2} = \left(29,~1\right) $ are linearly independent or dependent. | 2 |
2019 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 129 }{ 25 },~-\dfrac{ 203 }{ 50 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 379 }{ 100 },~0,~-\dfrac{ 561 }{ 100 }\right) $ . | 2 |
2020 | Find the sum of the vectors $ \vec{v_1} = \left(7,~2\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 2 |
2021 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 87 }{ 10 },~5\right) $ and $ \vec{v_2} = \left(\dfrac{ 43 }{ 10 },~\dfrac{ 5 }{ 2 }\right) $ . | 2 |
2022 | Find the angle between vectors $ \left(-5,~7\right)$ and $\left(-6,~4\right)$. | 2 |
2023 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(3,~10\right) $ . | 2 |
2024 | Find the projection of the vector $ \vec{v_1} = \left(2,~0\right) $ on the vector $ \vec{v_2} = \left(6,~3\right) $. | 2 |
2025 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-3,~0\right) $ . | 2 |
2026 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 2 |
2027 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 1 }{ 2 },~0\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 2 |
2028 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~0\right) $ and $ \vec{v_2} = \left(-2,~1,~8\right) $ . | 2 |
2029 | Find the angle between vectors $ \left(1,~-2\right)$ and $\left(4,~1\right)$. | 2 |
2030 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 2 |
2031 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~13\right) $ . | 2 |
2032 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~3\right) $ . | 2 |
2033 | Find the projection of the vector $ \vec{v_1} = \left(50,~57\right) $ on the vector $ \vec{v_2} = \left(29,~1\right) $. | 2 |
2034 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ . | 2 |
2035 | Find the angle between vectors $ \left(\dfrac{ 87 }{ 10 },~5\right)$ and $\left(\dfrac{ 43 }{ 10 },~\dfrac{ 5 }{ 2 }\right)$. | 2 |
2036 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(-6,~4\right) $ . | 2 |
2037 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~3\right) $ . | 2 |
2038 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~15\right) $ and $ \vec{v_2} = \left(24,~18\right) $ . | 2 |
2039 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~8\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ . | 2 |
2040 | Find the angle between vectors $ \left(2,~-5\right)$ and $\left(4,~2\right)$. | 2 |
2041 | Find the magnitude of the vector $ \| \vec{v} \| = \left(15,~-41\right) $ . | 2 |
2042 | Find the angle between vectors $ \left(57,~87\right)$ and $\left(67,~1\right)$. | 2 |
2043 | Find the sum of the vectors $ \vec{v_1} = \left(12,~3\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ . | 2 |
2044 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 2 |
2045 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-9\right) $ and $ \vec{v_2} = \left(7,~6\right) $ . | 2 |
2046 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~12\right) $ and $ \vec{v_2} = \left(0,~6\right) $ . | 2 |
2047 | Find the sum of the vectors $ \vec{v_1} = \left(15,~-41\right) $ and $ \vec{v_2} = \left(29,~37\right) $ . | 2 |
2048 | Find the sum of the vectors $ \vec{v_1} = \left(26,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 36 }{ 5 },~120\right) $ . | 2 |
2049 | Find the difference of the vectors $ \vec{v_1} = \left(9,~6\right) $ and $ \vec{v_2} = \left(8,~16\right) $ . | 2 |
2050 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~3\right) $ . | 2 |