Vectors – Solved Problems Database

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

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ID	Problem	Count
1051	Determine whether the vectors $ \vec{v_1} = \left(-5,~-4\right) $ and $ \vec{v_2} = \left(-2,~\dfrac{ 1 }{ 4 }\right) $ are linearly independent or dependent.	2
1052	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-9,~2\right) $ .	2
1053	Find the sum of the vectors $ \vec{v_1} = \left(8,~-4\right) $ and $ \vec{v_2} = \left(3,~1\right) $ .	2
1054	Find the angle between vectors $ \left(-\dfrac{ 131 }{ 200 },~-\dfrac{ 29 }{ 200 }\right)$ and $\left(\dfrac{ 77 }{ 1000 },~-\dfrac{ 409 }{ 1000 }\right)$.	2
1055	Find the angle between vectors $ \left(\dfrac{ 717 }{ 500 },~\dfrac{ 309 }{ 1000 }\right)$ and $\left(-\dfrac{ 19 }{ 125 },~\dfrac{ 887 }{ 1000 }\right)$.	2
1056	Find the sum of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(4,~5\right) $ .	2
1057	Determine whether the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(-23,~9\right) $ are linearly independent or dependent.	2
1058	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~4\right) $ .	2
1059	Determine whether the vectors $ \vec{v_1} = \left(1,~2,~5\right) $, $ \vec{v_2} = \left(2,~5,~1\right) $ and $ \vec{v_3} = \left(1,~5,~2\right)$ are linearly independent or dependent.	2
1060	Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 63961 }{ 125 },~\dfrac{ 35737 }{ 2000 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 304999 }{ 1000 },~-\dfrac{ 44319 }{ 200 }\right) $ .	2
1061	Find the sum of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(-4,~6\right) $ .	2
1062	Find the difference of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(3,~2\right) $ .	2
1063	Find the difference of the vectors $ \vec{v_1} = \left(5,~6\right) $ and $ \vec{v_2} = \left(-4,~-1\right) $ .	2
1064	Find the sum of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ .	2
1065	Find the sum of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(3,~2\right) $ .	2
1066	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~2\right) $ .	2
1067	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~3\right) $ .	2
1068	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-3\right) $ and $ \vec{v_2} = \left(-2,~-3\right) $ .	2
1069	Determine whether the vectors $ \vec{v_1} = \left(0,~2,~4\right) $, $ \vec{v_2} = \left(4,~0,~7\right) $ and $ \vec{v_3} = \left(4,~-2,~3\right)$ are linearly independent or dependent.	2
1070	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~-8\right) $ .	2
1071	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~7\right) $ .	2
1072	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(4,~3\right) $ .	2
1073	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-2\right) $ .	2
1074	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~-3\right) $ .	2
1075	Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-2,~-3\right) $ .	2
1076	Find the sum of the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(-7,~7\right) $ .	2
1077	Find the difference of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ .	2
1078	Find the projection of the vector $ \vec{v_1} = \left(6,~3\right) $ on the vector $ \vec{v_2} = \left(5,~9\right) $.	2
1079	Find the projection of the vector $ \vec{v_1} = \left(-8,~-8\right) $ on the vector $ \vec{v_2} = \left(-1,~-9\right) $.	2
1080	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~1\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ .	2
1081	Find the angle between vectors $ \left(16,~12\right)$ and $\left(33,~23\right)$.	2
1082	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(24,~10\right) $ .	2
1083	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~8\right) $ .	2
1084	Find the sum of the vectors $ \vec{v_1} = \left(-190,~321\right) $ and $ \vec{v_2} = \left(230,~80\right) $ .	2
1085	Find the difference of the vectors $ \vec{v_1} = \left(230,~80\right) $ and $ \vec{v_2} = \left(-190,~321\right) $ .	2
1086	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(420,~-241\right) $ .	2
1087	Find the difference of the vectors $ \vec{v_1} = \left(240,~20\right) $ and $ \vec{v_2} = \left(-140,~305\right) $ .	2
1088	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(380,~-285\right) $ .	2
1089	Find the difference of the vectors $ \vec{v_1} = \left(220,~20\right) $ and $ \vec{v_2} = \left(-150,~305.34\right) $ .	2
1090	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(370,~-285.34\right) $ .	2
1091	Find the difference of the vectors $ \vec{v_1} = \left(210,~30\right) $ and $ \vec{v_2} = \left(-150,~309.23\right) $ .	2
1092	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(360,~-279.23\right) $ .	2
1093	Find the difference of the vectors $ \vec{v_1} = \left(240,~40\right) $ and $ \vec{v_2} = \left(-190,~321.43\right) $ .	2
1094	Find the difference of the vectors $ \vec{v_1} = \left(240,~10\right) $ and $ \vec{v_2} = \left(-190,~321.43\right) $ .	2
1095	Find the difference of the vectors $ \vec{v_1} = \left(210,~30\right) $ and $ \vec{v_2} = \left(-190,~321.43\right) $ .	2
1096	Find the difference of the vectors $ \vec{v_1} = \left(220,~40\right) $ and $ \vec{v_2} = \left(-150,~309.23\right) $ .	2
1097	Find the difference of the vectors $ \vec{v_1} = \left(230,~6.67\right) $ and $ \vec{v_2} = \left(-150,~309.23\right) $ .	2
1098	Find the difference of the vectors $ \vec{v_1} = \left(220,~20\right) $ and $ \vec{v_2} = \left(-180,~318.7\right) $ .	2
1099	Find the difference of the vectors $ \vec{v_1} = \left(210,~40\right) $ and $ \vec{v_2} = \left(-190,~-231.43\right) $ .	2
1100	Find the difference of the vectors $ \vec{v_1} = \left(210,~40\right) $ and $ \vec{v_2} = \left(-190,~321.43\right) $ .	2