Vectors – Solved Problems Database

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

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ID	Problem	Count
1151	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(45,~0\right) $ .	2
1152	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-3,~2\right) $ and $ \vec{v_2} = \left(-3,~9,~-6\right) $ .	2
1153	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 2 }{ 5 },~-\dfrac{ 4 }{ 5 }\right) $ .	2
1154	Find the sum of the vectors $ \vec{v_1} = \left(6,~3,~4 \sqrt{ 5 }\right) $ and $ \vec{v_2} = \left(6,~0,~10 \sqrt{ 5 }\right) $ .	2
1155	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(12,~3,~14 \sqrt{ 5 }\right) $ .	2
1156	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0,~5\right) $ and $ \vec{v_2} = \left(5,~5 \sqrt{ 2 },~5\right) $ .	2
1157	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~0,~5\right) $ .	2
1158	Find the difference of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ .	2
1159	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~1\right) $ .	2
1160	Find the angle between vectors $ \left(2,~1\right)$ and $\left(4.1623,~2.1623\right)$.	2
1161	Find the sum of the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(9,~-1\right) $ .	2
1162	Find the difference of the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(0,~-1\right) $ .	2
1163	Find the difference of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(2,~-4\right) $ .	2
1164	Find the sum of the vectors $ \vec{v_1} = \left(0,~75\right) $ and $ \vec{v_2} = \left(250,~75\right) $ .	2
1165	Find the difference of the vectors $ \vec{v_1} = \left(30,~159\right) $ and $ \vec{v_2} = \left(\dfrac{ 27 }{ 2 },~\dfrac{ 85 }{ 2 }\right) $ .	2
1166	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~5\right) $ .	2
1167	Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~5\right) $ .	2
1168	Find the difference of the vectors $ \vec{v_1} = \left(-36,~4\right) $ and $ \vec{v_2} = \left(21,~13\right) $ .	2
1169	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ .	2
1170	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~-4\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ .	2
1171	Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~5\right) $ and $ \vec{v_2} = \left(2,~8\right) $ .	2
1172	Find the sum of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ .	2
1173	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~-4\right) $ and $ \vec{v_2} = \left(-10,~-10,~20\right) $ .	2
1174	Find the sum of the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(-5,~0\right) $ .	2
1175	Find the angle between vectors $ \left(0,~4\right)$ and $\left(0,~15\right)$.	2
1176	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 5017 }{ 10 },~\dfrac{ 34 }{ 5 }\right) $ .	2
1177	Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~18\right) $ and $ \vec{v_2} = \left(9,~3\right) $ .	2
1178	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-5,~-1\right) $ .	2
1179	Find the sum of the vectors $ \vec{v_1} = \left(-5,~-1\right) $ and $ \vec{v_2} = \left(3,~2\right) $ .	2
1180	Find the angle between vectors $ \left(6,~8\right)$ and $\left(2,~0\right)$.	2
1181	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(15,~7\right) $ .	2
1182	Find the sum of the vectors $ \vec{v_1} = \left(7,~2\right) $ and $ \vec{v_2} = \left(1,~4\right) $ .	2
1183	Find the sum of the vectors $ \vec{v_1} = \left(12,~3\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ .	2
1184	Find the difference of the vectors $ \vec{v_1} = \left(0,~9\right) $ and $ \vec{v_2} = \left(10,~4\right) $ .	2
1185	Find the difference of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(-5,~0\right) $ .	2
1186	Find the difference of the vectors $ \vec{v_1} = \left(-16,~12\right) $ and $ \vec{v_2} = \left(-10,~0\right) $ .	2
1187	Find the angle between vectors $ \left(7,~8\right)$ and $\left(5,~-3\right)$.	2
1188	Find the difference of the vectors $ \vec{v_1} = \left(-4,~2\right) $ and $ \vec{v_2} = \left(16,~12\right) $ .	2
1189	Find the difference of the vectors $ \vec{v_1} = \left(18,~-12\right) $ and $ \vec{v_2} = \left(-10,~0\right) $ .	2
1190	Find the sum of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ .	2
1191	Find the sum of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ .	2
1192	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~3\right) $ .	2
1193	Find the angle between vectors $ \left(-6,~-3\right)$ and $\left(-8,~4\right)$.	2
1194	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-5,~-3\right) $ and $ \vec{v_2} = \left(0,~-5,~-5\right) $ .	2
1195	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~0\right) $ and $ \vec{v_2} = \left(0,~-\dfrac{ 1 }{ 2 }\right) $ .	2
1196	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(- \dfrac{\sqrt{ 3 }}{ 2 },~-\dfrac{ 1 }{ 2 }\right) $ .	2
1197	Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(- \dfrac{\sqrt{ 3 }}{ 2 },~-\dfrac{ 1 }{ 2 }\right) $ .	2
1198	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~4\right) $ .	2
1199	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-23 \sqrt{ 2 },~-23 \sqrt{ 2 }\right) $ .	2
1200	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~-1\right) $ .	2