Vectors

(the database of solved problems)

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

Select category

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