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
1451	Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~4,~4\right) $ and $ \vec{v_2} = \left(4 \sqrt{ 2 },~4,~4\right) $ .	2
1452	Find the angle between vectors $ \left(5,~3\right)$ and $\left(-2,~4\right)$.	2
1453	Find the angle between vectors $ \left(-7,~7\right)$ and $\left(6,~-4\right)$.	2
1454	Find the difference of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(6,~-5\right) $ .	2
1455	Find the difference of the vectors $ \vec{v_1} = \left(-27,~21\right) $ and $ \vec{v_2} = \left(-12,~4\right) $ .	2
1456	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 329 }{ 10 },~\dfrac{ 189 }{ 10 }\right) $ .	2
1457	Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(4,~1\right) $ .	2
1458	Find the angle between vectors $ \left(-2,~-1\right)$ and $\left(-3,~-4\right)$.	2
1459	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~30\right) $ .	2
1460	Find the difference of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(0,~-5\right) $ .	2
1461	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~1\right) $ .	2
1462	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(18,~8\right) $ .	2
1463	Find the angle between vectors $ \left(18,~12\right)$ and $\left(6,~4\right)$.	2
1464	Find the sum of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(0,~2\right) $ .	2
1465	Find the difference of the vectors $ \vec{v_1} = \left(-3,~-12\right) $ and $ \vec{v_2} = \left(4,~9\right) $ .	2
1466	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(4,~5,~6\right) $ .	2
1467	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~-1\right) $ .	2
1468	Find the angle between vectors $ \left(1,~-1\right)$ and $\left(2,~1\right)$.	2
1469	Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ .	2
1470	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(150,~30\right) $ .	2
1471	Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(10,~5\right) $ are linearly independent or dependent.	2
1472	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~-12\right) $ .	2
1473	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(15,~8\right) $ .	2
1474	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-10,~20\right) $ .	2
1475	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~2,~3\right) $ .	2
1476	Find the angle between vectors $ \left(-3,~-1\right)$ and $\left(0,~-3\right)$.	2
1477	Find the difference of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ .	2
1478	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~1\right) $ .	2
1479	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-8,~-21\right) $ .	2
1480	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(2,~1\right) $ .	2
1481	Find the difference of the vectors $ \vec{v_1} = \left(-7,~-2\right) $ and $ \vec{v_2} = \left(-5,~8\right) $ .	2
1482	Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ .	2
1483	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-3\right) $ .	2
1484	Find the angle between vectors $ \left(3,~4\right)$ and $\left(-7,~5\right)$.	2
1485	Find the angle between vectors $ \left(2,~-1\right)$ and $\left(6,~4\right)$.	2
1486	Find the angle between vectors $ \left(4,~-1\right)$ and $\left(-3,~5\right)$.	2
1487	Find the projection of the vector $ \vec{v_1} = \left(2,~1\right) $ on the vector $ \vec{v_2} = \left(1,~2\right) $.	2
1488	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~2\right) $ .	2
1489	Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(0,~1\right) $ are linearly independent or dependent.	2
1490	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~0\right) $ .	2
1491	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~1\right) $ .	2
1492	Find the sum of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(4,~3\right) $ .	2
1493	Find the sum of the vectors $ \vec{v_1} = \left(-3,~-6\right) $ and $ \vec{v_2} = \left(4,~5\right) $ .	2
1494	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
1495	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-8\right) $ and $ \vec{v_2} = \left(0,~-9\right) $ .	2
1496	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0,~0\right) $ .	2
1497	Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-4,~0\right) $ and $ \vec{v_2} = \left(0,~0,~\dfrac{ 1 }{ 10 }\right) $ .	2
1498	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0,~0\right) $ .	2
1499	Find the sum of the vectors $ \vec{v_1} = \left(-12,~9\right) $ and $ \vec{v_2} = \left(-5,~-4\right) $ .	2
1500	Find the angle between vectors $ \left(0,~5\right)$ and $\left(-6,~1\right)$.	2