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
1251	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-9\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ .	2
1252	Find the difference of the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(-2,~0\right) $ .	2
1253	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~2 \sqrt{ 3 }\right) $ .	2
1254	Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-\dfrac{ 3 }{ 100 },~\dfrac{ 99 }{ 100 }\right) $ and $ \vec{v_2} = \left(0,~-1,~0\right) $ .	2
1255	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-10,~3\right) $ .	2
1256	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~1\right) $ .	2
1257	Find the angle between vectors $ \left(8,~-6\right)$ and $\left(-8,~-5\right)$.	2
1258	Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~5\right) $ .	2
1259	Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~6\right) $ .	2
1260	Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~7\right) $ .	2
1261	Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~9\right) $ .	2
1262	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~4\right) $ .	2
1263	Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(-24,~-6\right) $ .	2
1264	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~2\right) $ .	2
1265	Determine whether the vectors $ \vec{v_1} = \left(3,~12,~-21\right) $, $ \vec{v_2} = \left(2,~-1,~4\right) $ and $ \vec{v_3} = \left(0,~-10,~20\right)$ are linearly independent or dependent.	2
1266	Determine whether the vectors $ \vec{v_1} = \left(-5,~10\right) $ and $ \vec{v_2} = \left(-10,~20\right) $ are linearly independent or dependent.	2
1267	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~1\right) $ .	2
1268	Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(8,~2\right) $ .	2
1269	Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ .	2
1270	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-6,~4\right) $ .	2
1271	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(7,~35\right) $ .	2
1272	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~-1\right) $ .	2
1273	Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(2,~8\right) $ .	2
1274	Calculate the dot product of the vectors $ \vec{v_1} = \left(30,~-6\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	2
1275	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~-6\right) $ .	2
1276	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(25,~0\right) $ .	2
1277	Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~3,~2\right) $ and $ \vec{v_2} = \left(1,~3,~1\right) $ .	2
1278	Find the angle between vectors $ \left(\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right)$ and $\left(6,~8\right)$.	2
1279	Find the sum of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(12,~-18\right) $ .	2
1280	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ .	2
1281	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ .	2
1282	Find the angle between vectors $ \left(-4,~3\right)$ and $\left(3,~8\right)$.	2
1283	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-18,~14\right) $ .	2
1284	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~-1\right) $ .	2
1285	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1\right) $ and $ \vec{v_2} = \left(6,~2\right) $ .	2
1286	Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(6,~2\right) $ .	2
1287	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~20\right) $ .	2
1288	Find the projection of the vector $ \vec{v_1} = \left(9,~-7\right) $ on the vector $ \vec{v_2} = \left(-10,~7\right) $.	2
1289	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ .	2
1290	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 1 }{ 8 }\right) $ .	2
1291	Find the sum of the vectors $ \vec{v_1} = \left(-1,~-4,~2\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ .	2
1292	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(1,~-2,~3\right) $ .	2
1293	Find the angle between vectors $ \left(3,~9\right)$ and $\left(-9,~5\right)$.	2
1294	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~-12\right) $ .	2
1295	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~2\right) $ .	2
1296	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~0\right) $ .	2
1297	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~7\right) $ and $ \vec{v_2} = \left(7,~8\right) $ .	2
1298	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~4\right) $ .	2
1299	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~2\right) $ .	2
1300	Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-2\right) $ and $ \vec{v_2} = \left(7,~-2\right) $ .	2