Vectors

(the database of solved problems)

All the problems and solutions shown below were generated using the Vectors Calculator.

Select category

ID	Problem	Count
2001	Find the angle between vectors $ \left(4,~-4\right)$ and $\left(-12,~-12\right)$.	2
2002	Find the angle between vectors $ \left(4,~-4\right)$ and $\left(1,~-4\right)$.	2
2003	Find the angle between vectors $ \left(4,~-4\right)$ and $\left(-1,~-3\right)$.	2
2004	Calculate the dot product of the vectors $ \vec{v_1} = \left(33.3793,~536.4621\right) $ and $ \vec{v_2} = \left(44.7848,~528.8015\right) $ .	2
2005	Find the projection of the vector $ \vec{v_1} = \left(33.3793,~536.4621\right) $ on the vector $ \vec{v_2} = \left(44.7848,~528.8015\right) $.	2
2006	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~8\right) $ .	2
2007	Find the projection of the vector $ \vec{v_1} = \left(-1,~4\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 7 }{ 2 },~-\dfrac{ 5 }{ 4 }\right) $.	2
2008	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-46,~-42\right) $ .	2
2009	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3,~5\right) $ and $ \vec{v_2} = \left(-2,~4,~-1\right) $ .	2
2010	Find the angle between vectors $ \left(-3,~-7\right)$ and $\left(4,~-4\right)$.	2
2011	Find the sum of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ .	2
2012	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ .	2
2013	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~0\right) $ and $ \vec{v_2} = \left(0,~2\right) $ .	2
2014	Find the projection of the vector $ \vec{v_1} = \left(-19,~-9,~16\right) $ on the vector $ \vec{v_2} = \left(-6,~-2,~6\right) $.	2
2015	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 14 }{ 5 },~-1\right) $ and $ \vec{v_2} = \left(0,~2\right) $ .	2
2016	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 14 }{ 5 },~1\right) $ and $ \vec{v_2} = \left(-\dfrac{ 17 }{ 10 },~-\dfrac{ 47 }{ 10 }\right) $ .	2
2017	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 173 }{ 10 },~10\right) $ and $ \vec{v_2} = \left(-\dfrac{ 63 }{ 10 },~\dfrac{ 68 }{ 5 }\right) $ .	2
2018	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~2\right) $ .	2
2019	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 173 }{ 10 },~10\right) $ .	2
2020	Find the angle between vectors $ \left(\dfrac{ 173 }{ 10 },~10\right)$ and $\left(-\dfrac{ 63 }{ 10 },~\dfrac{ 68 }{ 5 }\right)$.	2
2021	Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ are linearly independent or dependent.	2
2022	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 71 }{ 1000 },~\dfrac{ 833 }{ 1000 },~\dfrac{ 137 }{ 200 }\right) $ .	2
2023	Find the sum of the vectors $ \vec{v_1} = \left(15,~14\right) $ and $ \vec{v_2} = \left(4,~11\right) $ .	2
2024	Find the projection of the vector $ \vec{v_1} = \left(15.898,~25.441\right) $ on the vector $ \vec{v_2} = \left(6.84,~18.79\right) $.	2
2025	Find the difference of the vectors $ \vec{v_1} = \left(24,~10\right) $ and $ \vec{v_2} = \left(-15,~20\right) $ .	2
2026	Find the projection of the vector $ \vec{v_1} = \left(3,~-2\right) $ on the vector $ \vec{v_2} = \left(5,~1\right) $.	2
2027	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~25\right) $ .	2
2028	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 5 }{ 13 },~\dfrac{ 12 }{ 13 }\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ .	2
2029	Find the angle between vectors $ \left(\dfrac{ 5 }{ 13 },~\dfrac{ 12 }{ 13 }\right)$ and $\left(-4,~8\right)$.	2
2030	Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(2,~1\right) $ .	2
2031	Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~-6,~9\right) $ and $ \vec{v_2} = \left(5,~-3,~4\right) $ .	2
2032	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ .	2
2033	Find the sum of the vectors $ \vec{v_1} = \left(0.2,~30\right) $ and $ \vec{v_2} = \left(0.2,~120\right) $ .	2
2034	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~3\right) $ .	2
2035	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~2\right) $ and $ \vec{v_2} = \left(3,~-4,~2\right) $ .	2
2036	Find the sum of the vectors $ \vec{v_1} = \left(4,~0\right) $ and $ \vec{v_2} = \left(1,~2\right) $ .	2
2037	Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(4,~0\right) $ .	2
2038	Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ .	2
2039	Find the sum of the vectors $ \vec{v_1} = \left(4,~0\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ .	2
2040	Find the sum of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(2,~2\right) $ .	2
2041	Find the difference of the vectors $ \vec{v_1} = \left(0,~-4\right) $ and $ \vec{v_2} = \left(2,~-5\right) $ .	2
2042	Find the sum of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(3,~2\right) $ .	2
2043	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~5\right) $ .	2
2044	Find the angle between vectors $ \left(\dfrac{ 26 }{ 5 },~-\dfrac{ 43 }{ 10 }\right)$ and $\left(-\dfrac{ 71 }{ 10 },~-\dfrac{ 16 }{ 5 }\right)$.	2
2045	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 25 }{ 4 },~-\dfrac{ 19 }{ 5 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 23 }{ 5 },~\dfrac{ 11 }{ 4 }\right) $ .	2
2046	Find the projection of the vector $ \vec{v_1} = \left(-2,~6\right) $ on the vector $ \vec{v_2} = \left(-9,~-3\right) $.	2
2047	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~-2\right) $ .	2
2048	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 43 }{ 5 },~-\dfrac{ 13 }{ 2 }\right) $ .	2
2049	Find the angle between vectors $ \left(3,~0\right)$ and $\left(2,~0\right)$.	2
2050	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~0\right) $ .	2