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
1401	Find the angle between vectors $ \left(2,~1\right)$ and $\left(1,~-3\right)$.	2
1402	Find the sum of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	2
1403	Find the sum of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(2,~-7\right) $ .	2
1404	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(4,~1\right) $ .	2
1405	Find the sum of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ .	2
1406	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ .	2
1407	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(15,~-15\right) $ .	2
1408	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~6\right) $ .	2
1409	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
1410	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-6,~-3\right) $ .	2
1411	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(2,~2\right) $ .	2
1412	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ .	2
1413	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ .	2
1414	Find the angle between vectors $ \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right)$ and $\left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right)$.	2
1415	Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(5,~0\right) $ .	2
1416	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~3\right) $ .	2
1417	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~1\right) $ .	2
1418	Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(2,~6\right) $ .	2
1419	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~-2\right) $ .	2
1420	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-7,~-9\right) $ .	2
1421	Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~1\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ .	2
1422	Find the difference of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(3,~-5\right) $ .	2
1423	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-12\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 4 }{ 5 }\right) $ .	2
1424	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~5\right) $ .	2
1425	Find the difference of the vectors $ \vec{v_1} = \left(-3,~-6\right) $ and $ \vec{v_2} = \left(-4,~-9\right) $ .	2
1426	Find the angle between vectors $ \left(2,~0\right)$ and $\left(1,~3\right)$.	2
1427	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~7\right) $ and $ \vec{v_2} = \left(7,~1\right) $ .	2
1428	Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~8\right) $ and $ \vec{v_2} = \left(1,~1\right) $ .	2
1429	Find the angle between vectors $ \left(-8,~8\right)$ and $\left(1,~1\right)$.	2
1430	Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~8\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ .	2
1431	Find the angle between vectors $ \left(-8,~8\right)$ and $\left(1,~-1\right)$.	2
1432	Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-5\right) $ and $ \vec{v_2} = \left(6,~5\right) $ .	2
1433	Find the sum of the vectors $ \vec{v_1} = \left(10,~1\right) $ and $ \vec{v_2} = \left(1,~10\right) $ .	2
1434	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ .	2
1435	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~3\right) $ .	2
1436	Find the sum of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ .	2
1437	Find the sum of the vectors $ \vec{v_1} = \left(2,~9\right) $ and $ \vec{v_2} = \left(2,~0\right) $ .	2
1438	Find the angle between vectors $ \left(2,~0\right)$ and $\left(2,~8\right)$.	2
1439	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(7,~1\right) $ .	2
1440	Find the angle between vectors $ \left(2,~-1\right)$ and $\left(7,~1\right)$.	2
1441	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-4\right) $ .	2
1442	Find the difference of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-4,~-4\right) $ .	2
1443	Find the difference of the vectors $ \vec{v_1} = \left(-4,~-4\right) $ and $ \vec{v_2} = \left(3,~-4\right) $ .	2
1444	Determine whether the vectors $ \vec{v_1} = \left(1,~2,~4\right) $, $ \vec{v_2} = \left(1,~3,~5\right) $ and $ \vec{v_3} = \left(2,~1,~5\right)$ are linearly independent or dependent.	2
1445	Find the sum of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(10,~0\right) $ .	2
1446	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~-1\right) $ .	2
1447	Find the angle between vectors $ \left(1,~-12\right)$ and $\left(-\dfrac{ 1 }{ 4 },~3\right)$.	2
1448	Determine whether the vectors $ \vec{v_1} = \left(1,~-12\right) $ and $ \vec{v_2} = \left(-\dfrac{ 1 }{ 4 },~3\right) $ are linearly independent or dependent.	2
1449	Find the sum of the vectors $ \vec{v_1} = \left(0,~2\right) $ and $ \vec{v_2} = \left(1,~4\right) $ .	2
1450	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(20,~0\right) $ .	2