Vectors

(the database of solved problems)

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

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ID	Problem	Count
2051	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~-2\right) $ .	2
2052	Find the difference of the vectors $ \vec{v_1} = \left(-7,~-1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ .	2
2053	Find the projection of the vector $ \vec{v_1} = \left(-9,~-4\right) $ on the vector $ \vec{v_2} = \left(-11,~-8\right) $.	2
2054	Find the sum of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(7,~1\right) $ .	2
2055	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~6\right) $ .	2
2056	Find the angle between vectors $ \left(4,~6\right)$ and $\left(7,~0\right)$.	2
2057	Find the angle between vectors $ \left(-8,~-4,~0\right)$ and $\left(-3,~9,~7\right)$.	2
2058	Determine whether the vectors $ \vec{v_1} = \left(-6,~4\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ are linearly independent or dependent.	2
2059	Find the projection of the vector $ \vec{v_1} = \left(15,~30\right) $ on the vector $ \vec{v_2} = \left(-1,~4\right) $.	2
2060	Calculate the cross product of the vectors $ \vec{v_1} = \left(-8,~-3,~3\right) $ and $ \vec{v_2} = \left(-2,~-2,~-8\right) $ .	2
2061	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~2\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ .	2
2062	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-2\right) $ .	2
2063	Find the difference of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(5,~0\right) $ .	2
2064	Find the difference of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ .	2
2065	Find the difference of the vectors $ \vec{v_1} = \left(6,~4\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ .	2
2066	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~-4\right) $ .	2
2067	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(7,~10\right) $ .	2
2068	Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(1,~-2\right) $ .	2
2069	Find the angle between vectors $ \left(4,~2\right)$ and $\left(1,~-2\right)$.	2
2070	Find the sum of the vectors $ \vec{v_1} = \left(-5,~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(2,~-\dfrac{ 1 }{ 4 }\right) $ .	2
2071	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-2,~4\right) $ and $ \vec{v_2} = \left(-1,~3,~-2\right) $ .	2
2072	Find the sum of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(2,~1\right) $ .	2
2073	Find the difference of the vectors $ \vec{v_1} = \left(-18,~18\right) $ and $ \vec{v_2} = \left(4,~25\right) $ .	2
2074	Find the difference of the vectors $ \vec{v_1} = \left(-15,~40\right) $ and $ \vec{v_2} = \left(-2,~-8\right) $ .	2
2075	Find the angle between vectors $ \left(\dfrac{ 62 }{ 5 },~45\right)$ and $\left(\dfrac{ 26 }{ 5 },~90\right)$.	2
2076	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
2077	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
2078	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ .	2
2079	Find the angle between vectors $ \left(-21.58,~-20.84\right)$ and $\left(-9.72,~-20.85\right)$.	2
2080	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0.2103,~0.7071,~0.6751\right) $ .	2
2081	Find the difference of the vectors $ \vec{v_1} = \left(0,~-3\right) $ and $ \vec{v_2} = \left(0,~5\right) $ .	2
2082	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~0\right) $ .	2
2083	Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(10,~60\right) $ .	2
2084	Find the sum of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ .	2
2085	Find the sum of the vectors $ \vec{v_1} = \left(6,~18\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ .	2
2086	Find the angle between vectors $ \left(-3,~-2\right)$ and $\left(5,~-7\right)$.	2
2087	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~-2\right) $ .	2
2088	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~-6\right) $ .	2
2089	Determine whether the vectors $ \vec{v_1} = \left(1,~-6\right) $ and $ \vec{v_2} = \left(-15,~8\right) $ are linearly independent or dependent.	2
2090	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
2091	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(17,~8\right) $ .	2
2092	Find the sum of the vectors $ \vec{v_1} = \left(-3,~8\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ .	2
2093	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(35,~21\right) $ .	2
2094	Determine whether the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ are linearly independent or dependent.	2
2095	Find the angle between vectors $ \left(3,~-4\right)$ and $\left(-5,~-12\right)$.	2
2096	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~7\right) $ .	2
2097	Find the sum of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	2
2098	Find the difference of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(3,~-4\right) $ .	2
2099	Find the difference of the vectors $ \vec{v_1} = \left(-5,~-2\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ .	2
2100	Find the difference of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ .	2