Vectors

(the database of solved problems)

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

Select category

ID	Problem	Count
2101	Find the projection of the vector $ \vec{v_1} = \left(4,~1\right) $ on the vector $ \vec{v_2} = \left(2,~5\right) $.	2
2102	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ .	2
2103	Find the angle between vectors $ \left(4,~1\right)$ and $\left(2,~5\right)$.	2
2104	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-6,~3\right) $ .	2
2105	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~3\right) $ .	2
2106	Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(-1,~-6\right) $ .	2
2107	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-5,~7\right) $ .	2
2108	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~1,~-2\right) $ .	2
2109	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2000,~45\right) $ .	2
2110	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(-2,~6\right) $ .	2
2111	Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~2\right) $ and $ \vec{v_2} = \left(2,~4,~2\right) $ .	2
2112	Find the angle between vectors $ \left(3,~1,~2\right)$ and $\left(2,~4,~2\right)$.	2
2113	Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ .	2
2114	Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(6,~-4\right) $ .	2
2115	Calculate the dot product of the vectors $ \vec{v_1} = \left(240,~310\right) $ and $ \vec{v_2} = \left(\dfrac{ 14 }{ 5 },~\dfrac{ 74 }{ 25 }\right) $ .	2
2116	Find the sum of the vectors $ \vec{v_1} = \left(7,~1\right) $ and $ \vec{v_2} = \left(-5,~-3\right) $ .	2
2117	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
2118	Find the angle between vectors $ \left(2,~-5\right)$ and $\left(-3,~8\right)$.	2
2119	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~-1\right) $ .	2
2120	Find the sum of the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(3,~3\right) $ .	2
2121	Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-2,~-5\right) $ .	2
2122	Find the sum of the vectors $ \vec{v_1} = \left(-1,~-4\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ .	2
2123	Find the sum of the vectors $ \vec{v_1} = \left(3130,~108\right) $ and $ \vec{v_2} = \left(2860,~168\right) $ .	2
2124	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3130,~108\right) $ .	2
2125	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~3\right) $ .	2
2126	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-7,~1\right) $ .	2
2127	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(30,~12\right) $ .	2
2128	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~0\right) $ .	2
2129	Find the angle between vectors $ \left(4,~-8\right)$ and $\left(-2,~4\right)$.	2
2130	Determine whether the vectors $ \vec{v_1} = \left(4,~-8\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ are linearly independent or dependent.	2
2131	Find the sum of the vectors $ \vec{v_1} = \left(4,~-7\right) $ and $ \vec{v_2} = \left(-2,~6\right) $ .	2
2132	Find the sum of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ .	2
2133	Find the angle between vectors $ \left(1,~5,~-1\right)$ and $\left(5,~-1,~1\right)$.	2
2134	Find the angle between vectors $ \left(1,~5,~-1\right)$ and $\left(-1,~1,~4\right)$.	2
2135	Find the angle between vectors $ \left(1,~5,~-1\right)$ and $\left(-1,~-1,~5\right)$.	2
2136	Find the angle between vectors $ \left(-5,~-1,~1\right)$ and $\left(5,~-1,~1\right)$.	2
2137	Find the angle between vectors $ \left(-5,~-1,~1\right)$ and $\left(-1,~1,~4\right)$.	2
2138	Find the angle between vectors $ \left(5,~-1,~1\right)$ and $\left(-1,~1,~4\right)$.	2
2139	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-7,~4\right) $ .	2
2140	Find the angle between vectors $ \left(-7,~4\right)$ and $\left(-1,~-4\right)$.	2
2141	Find the sum of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ .	2
2142	Find the difference of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(-3,~7\right) $ .	2
2143	Find the angle between vectors $ \left(9,~-8\right)$ and $\left(2,~-12\right)$.	2
2144	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~-11\right) $ .	2
2145	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~6\right) $ .	2
2146	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~5\right) $ .	2
2147	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3130,~108\right) $ .	2
2148	Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(-3,~8\right) $ .	2
2149	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-4\right) $ and $ \vec{v_2} = \left(-3,~8\right) $ .	2
2150	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~1\right) $ .	2