Vectors

(the database of solved problems)

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

Select category

ID	Problem	Count
2151	Find the difference of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(-8,~-3\right) $ .	2
2152	Find the angle between vectors $ \left(3,~5,~-7\right)$ and $\left(-3,~4,~-2\right)$.	2
2153	Calculate the dot product of the vectors $ \vec{v_1} = \left(11,~1\right) $ and $ \vec{v_2} = \left(11,~1\right) $ .	2
2154	Find the angle between vectors $ \left(2,~0\right)$ and $\left(2,~3\right)$.	2
2155	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-10,~5\right) $ and $ \vec{v_2} = \left(0,~-1.688,~4.24\right) $ .	2
2156	Find the projection of the vector $ \vec{v_1} = \left(6,~17\right) $ on the vector $ \vec{v_2} = \left(11,~-11\right) $.	2
2157	Determine whether the vectors $ \vec{v_1} = \left(6,~17\right) $ and $ \vec{v_2} = \left(11,~-11\right) $ are linearly independent or dependent.	2
2158	Determine whether the vectors $ \vec{v_1} = \left(1,~1,~0\right) $, $ \vec{v_2} = \left(1,~2,~1\right) $ and $ \vec{v_3} = \left(0,~1,~1\right)$ are linearly independent or dependent.	2
2159	Find the sum of the vectors $ \vec{v_1} = \left(4,~-1\right) $ and $ \vec{v_2} = \left(7,~5\right) $ .	2
2160	Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(1,~-6\right) $ .	2
2161	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~-4\right) $ .	2
2162	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~3\right) $ .	2
2163	Find the sum of the vectors $ \vec{v_1} = \left(5,~-3\right) $ and $ \vec{v_2} = \left(-5,~7\right) $ .	2
2164	Find the sum of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(4,~1\right) $ .	2
2165	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(3,~6\right) $ .	2
2166	Find the angle between vectors $ \left(-7,~3\right)$ and $\left(9,~1\right)$.	2
2167	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-\sqrt{ 3 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\sqrt{ 2 },~1,~\dfrac{ 2 }{ 3 }\right) $ .	2
2168	Find the angle between vectors $ \left(1,~-\sqrt{ 3 },~\dfrac{ 3 }{ 2 }\right)$ and $\left(\sqrt{ 2 },~1,~\dfrac{ 2 }{ 3 }\right)$.	2
2169	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~5\right) $ and $ \vec{v_2} = \left(-6,~-6\right) $ .	2
2170	Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-3,~-1\right) $ .	2
2171	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~5\right) $ .	2
2172	Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(-7,~6\right) $ .	2
2173	Find the difference of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~-2,~2\right) $ .	2
2174	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~2\right) $ and $ \vec{v_2} = \left(0,~1,~-2\right) $ .	2
2175	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-4,~0\right) $ and $ \vec{v_2} = \left(-3,~8,~0\right) $ .	2
2176	Find the difference of the vectors $ \vec{v_1} = \left(-2,~2\right) $ and $ \vec{v_2} = \left(-1,~-1\right) $ .	2
2177	Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~2\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ .	2
2178	Find the sum of the vectors $ \vec{v_1} = \left(-9,~9\right) $ and $ \vec{v_2} = \left(-4,~-5\right) $ .	2
2179	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-5,~-3\right) $ .	2
2180	Find the angle between vectors $ \left(-6,~3\right)$ and $\left(3,~5\right)$.	2
2181	Find the projection of the vector $ \vec{v_1} = \left(6,~9\right) $ on the vector $ \vec{v_2} = \left(3,~-2\right) $.	2
2182	Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~1\right) $ and $ \vec{v_2} = \left(2,~-4\right) $ .	2
2183	Calculate the dot product of the vectors $ \vec{v_1} = \left(15,~15\right) $ and $ \vec{v_2} = \left(-5,~4\right) $ .	2
2184	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~4\right) $ and $ \vec{v_2} = \left(-7,~1\right) $ .	2
2185	Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(4,~4\right) $ .	2
2186	Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ .	2
2187	Find the difference of the vectors $ \vec{v_1} = \left(2,~7\right) $ and $ \vec{v_2} = \left(6,~3\right) $ .	2
2188	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~3\right) $ .	2
2189	Find the difference of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(0,~2\right) $ .	2
2190	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(0,~2\right) $ .	2
2191	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-24,~7\right) $ .	2
2192	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-7,~24\right) $ .	2
2193	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ .	2
2194	Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 23 }{ 5 },~-\dfrac{ 41 }{ 5 },~\dfrac{ 49 }{ 5 }\right) $ and $ \vec{v_2} = \left(-9,~-\dfrac{ 33 }{ 10 },~\dfrac{ 22 }{ 5 }\right) $ .	2
2195	Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~\dfrac{ 9 }{ 2 },~2\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 13 }{ 5 },~\dfrac{ 13 }{ 5 }\right) $ .	2
2196	Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~4.5,~2\right) $ and $ \vec{v_2} = \left(0,~2.6,~2.6\right) $ .	2
2197	Find the angle between vectors $ \left(9,~-7\right)$ and $\left(-10,~7\right)$.	2
2198	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~-1\right) $ .	2
2199	Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~6\right) $ and $ \vec{v_2} = \left(-25.44,~-13.36,~20.44\right) $ .	2
2200	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