Vectors – Solved Problems Database

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

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ID	Problem	Count
1201	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ .	2
1202	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~0\right) $ and $ \vec{v_2} = \left(4,~5\right) $ .	2
1203	Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~1\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ .	2
1204	Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~5\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ .	2
1205	Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~3,~-4\right) $ and $ \vec{v_2} = \left(-2,~3,~-7\right) $ .	2
1206	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~-2\right) $ and $ \vec{v_2} = \left(1,~2,~-2\right) $ .	2
1207	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(9,~-7\right) $ .	2
1208	Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(7,~6\right) $ .	2
1209	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(2,~3\right) $ .	2
1210	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(5,~-7\right) $ .	2
1211	Find the sum of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(6,~0\right) $ .	2
1212	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~0\right) $ .	2
1213	Find the angle between vectors $ \left(-2,~-3\right)$ and $\left(6,~-1\right)$.	2
1214	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(2,~4\right) $ .	2
1215	Find the difference of the vectors $ \vec{v_1} = \left(8,~-8\right) $ and $ \vec{v_2} = \left(-5,~8\right) $ .	2
1216	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~17\right) $ .	2
1217	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~-15\right) $ .	2
1218	Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 50 },~\dfrac{ 3 }{ 40 },~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 433 }{ 2 },~125\right) $ .	2
1219	Find the angle between vectors $ \left(0,~10\right)$ and $\left(0,~15\right)$.	2
1220	Find the sum of the vectors $ \vec{v_1} = \left(32,~40\right) $ and $ \vec{v_2} = \left(42,~36\right) $ .	2
1221	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(74,~76\right) $ .	2
1222	Find the projection of the vector $ \vec{v_1} = \left(-3,~0\right) $ on the vector $ \vec{v_2} = \left(5,~0\right) $.	2
1223	Find the difference of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(-8,~-20\right) $ .	2
1224	Find the sum of the vectors $ \vec{v_1} = \left(0,~-30\right) $ and $ \vec{v_2} = \left(-9,~-27\right) $ .	2
1225	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(-\dfrac{ 9 }{ 2 },~0\right) $ .	2
1226	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 2 },~0\right) $ .	2
1227	Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 2 },~0\right) $ .	2
1228	Calculate the dot product of the vectors $ \vec{v_1} = \left(22,~15\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ .	2
1229	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~10\right) $ and $ \vec{v_2} = \left(-\dfrac{ 3 }{ 2 },~\dfrac{ 3 }{ 5 }\right) $ .	2
1230	Find the angle between vectors $ \left(-7,~8\right)$ and $\left(1,~0\right)$.	2
1231	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-7,~8\right) $ .	2
1232	Find the angle between vectors $ \left(-7,~8\right)$ and $\left(5,~3\right)$.	2
1233	Find the difference of the vectors $ \vec{v_1} = \left(16,~-8\right) $ and $ \vec{v_2} = \left(18,~3\right) $ .	2
1234	Find the angle between vectors $ \left(7,~5\right)$ and $\left(-4,~-2\right)$.	2
1235	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 333 }{ 100 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 333 }{ 100 },~120\right) $ .	2
1236	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 333 }{ 100 },~0\right) $ .	2
1237	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 333 }{ 100 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 333 }{ 100 },~120\right) $ .	2
1238	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~2,~-4\right) $ .	2
1239	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0,~-\dfrac{ 707107 }{ 25000 }\right) $ .	2
1240	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-3\right) $ .	2
1241	Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ .	2
1242	Find the angle between vectors $ \left(1,~2\right)$ and $\left(-6,~3\right)$.	2
1243	Find the angle between vectors $ \left(2,~0\right)$ and $\left(1,~1\right)$.	2
1244	Find the sum of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ .	2
1245	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(67,~85\right) $ .	2
1246	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~12\right) $ .	2
1247	Find the sum of the vectors $ \vec{v_1} = \left(-4,~12\right) $ and $ \vec{v_2} = \left(6,~8\right) $ .	2
1248	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 24 }{ 5 },~-4\right) $ .	2
1249	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~7\right) $ .	2
1250	Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~1\right) $ and $ \vec{v_2} = \left(9,~6\right) $ .	2