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
1551	Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 17043 }{ 10 },~\dfrac{ 31 }{ 5 },~-\dfrac{ 5772 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8611 }{ 5 },~\dfrac{ 13 }{ 2 },~-\dfrac{ 5748 }{ 5 }\right) $ .	2
1552	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~1\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ .	2
1553	Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ .	2
1554	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
1555	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ .	2
1556	Find the angle between vectors $ \left(0,~1\right)$ and $\left(1,~1\right)$.	2
1557	Determine whether the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent.	2
1558	Find the projection of the vector $ \vec{v_1} = \left(0,~1\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $.	2
1559	Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~2\right) $ .	2
1560	Find the sum of the vectors $ \vec{v_1} = \left(3,~7\right) $ and $ \vec{v_2} = \left(-8,~4\right) $ .	2
1561	Find the angle between vectors $ \left(9,~6\right)$ and $\left(-4,~5\right)$.	2
1562	Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~6\right) $ and $ \vec{v_2} = \left(-4,~6\right) $ .	2
1563	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~-5\right) $ .	2
1564	Find the difference of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(-1,~-5\right) $ .	2
1565	Find the sum of the vectors $ \vec{v_1} = \left(120000,~30\right) $ and $ \vec{v_2} = \left(40000,~-90\right) $ .	2
1566	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(1,~-4\right) $ .	2
1567	Find the difference of the vectors $ \vec{v_1} = \left(-8,~-3\right) $ and $ \vec{v_2} = \left(-5,~-8\right) $ .	2
1568	Find the difference of the vectors $ \vec{v_1} = \left(-1,~9\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ .	2
1569	Find the angle between vectors $ \left(\dfrac{ 7 }{ 5 },~\dfrac{ 121 }{ 50 }\right)$ and $\left(\dfrac{ 19 }{ 20 },~\dfrac{ 33 }{ 20 }\right)$.	2
1570	Find the angle between vectors $ \left(1,~0\right)$ and $\left(0,~1\right)$.	2
1571	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(30,~0\right) $ .	2
1572	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ .	2
1573	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-12,~5\right) $ .	2
1574	Determine whether the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-4,~0\right) $ are linearly independent or dependent.	2
1575	Find the projection of the vector $ \vec{v_1} = \left(3,~0\right) $ on the vector $ \vec{v_2} = \left(-2,~0\right) $.	2
1576	Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~4\right) $ and $ \vec{v_2} = \left(8,~-2\right) $ .	2
1577	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~-2\right) $ .	2
1578	Find the sum of the vectors $ \vec{v_1} = \left(-1,~-4,~2\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ .	2
1579	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
1580	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(-8,~5,~6\right) $ .	2
1581	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 2069 }{ 100 },~\dfrac{ 857 }{ 100 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 997 }{ 100 },~\dfrac{ 1499 }{ 50 }\right) $ .	2
1582	Find the sum of the vectors $ \vec{v_1} = \left(-4,~5\right) $ and $ \vec{v_2} = \left(2,~-4\right) $ .	2
1583	Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-1,~-5\right) $ .	2
1584	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ .	2
1585	Find the projection of the vector $ \vec{v_1} = \left(1,~-2,~1\right) $ on the vector $ \vec{v_2} = \left(4,~-4,~7\right) $.	2
1586	Find the projection of the vector $ \vec{v_1} = \left(2 \sqrt{ 3 },~2\right) $ on the vector $ \vec{v_2} = \left(6,~0\right) $.	2
1587	Find the angle between vectors $ \left(1,~3\right)$ and $\left(2,~1\right)$.	2
1588	Find the angle between vectors $ \left(3,~-4\right)$ and $\left(1,~0\right)$.	2
1589	Find the projection of the vector $ \vec{v_1} = \left(-8,~4\right) $ on the vector $ \vec{v_2} = \left(7,~-6\right) $.	2
1590	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(37,~40\right) $ .	2
1591	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~5\right) $ .	2
1592	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~2\right) $ .	2
1593	Find the sum of the vectors $ \vec{v_1} = \left(5,~5\right) $ and $ \vec{v_2} = \left(2,~6\right) $ .	2
1594	Find the projection of the vector $ \vec{v_1} = \left(5,~5\right) $ on the vector $ \vec{v_2} = \left(2,~6\right) $.	2
1595	Find the difference of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(-9,~16\right) $ .	2
1596	Find the difference of the vectors $ \vec{v_1} = \left(7,~4\right) $ and $ \vec{v_2} = \left(-9,~28\right) $ .	2
1597	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ .	2
1598	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~5,~5\right) $ and $ \vec{v_2} = \left(5,~0,~-5\right) $ .	2
1599	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~4\right) $ .	2
1600	Find the sum of the vectors $ \vec{v_1} = \left(1,~5\right) $ and $ \vec{v_2} = \left(43,~0\right) $ .	2