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
1601	Find the sum of the vectors $ \vec{v_1} = \left(1,~5\right) $ and $ \vec{v_2} = \left(4,~3\right) $ .	2
1602	Find the sum of the vectors $ \vec{v_1} = \left(-1,~-5\right) $ and $ \vec{v_2} = \left(4,~3\right) $ .	2
1603	Find the sum of the vectors $ \vec{v_1} = \left(7,~8\right) $ and $ \vec{v_2} = \left(9,~0\right) $ .	2
1604	Find the sum of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(9,~0\right) $ .	2
1605	Find the difference of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(9,~0\right) $ .	2
1606	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(9,~0\right) $ .	2
1607	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~1\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ .	2
1608	Calculate the dot product of the vectors $ \vec{v_1} = \left(-18,~3\right) $ and $ \vec{v_2} = \left(1,~6\right) $ .	2
1609	Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ .	2
1610	Determine whether the vectors $ \vec{v_1} = \left(-6,~6\right) $ and $ \vec{v_2} = \left(8,~8\right) $ are linearly independent or dependent.	2
1611	Determine whether the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(18,~-12\right) $ are linearly independent or dependent.	2
1612	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~-4\right) $ .	2
1613	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(9,~8\right) $ .	2
1614	Find the projection of the vector $ \vec{v_1} = \left(1,~1\right) $ on the vector $ \vec{v_2} = \left(8,~3\right) $.	2
1615	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(14,~4\right) $ .	2
1616	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~3\right) $ .	2
1617	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-21,~28\right) $ .	2
1618	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~3\right) $ and $ \vec{v_2} = \left(0,~3,~-1\right) $ .	2
1619	Calculate the dot product of the vectors $ \vec{v_1} = \left(3020,~2800\right) $ and $ \vec{v_2} = \left(1,~1\right) $ .	2
1620	Find the projection of the vector $ \vec{v_1} = \left(3020,~2800\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $.	2
1621	Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(4,~2\right) $ .	2
1622	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0,~1\right) $ .	2
1623	Find the angle between vectors $ \left(-2,~-4\right)$ and $\left(4,~8\right)$.	2
1624	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-9,~7\right) $ .	2
1625	Find the angle between vectors $ \left(-9,~7\right)$ and $\left(7,~5\right)$.	2
1626	Determine whether the vectors $ \vec{v_1} = \left(-9,~7\right) $ and $ \vec{v_2} = \left(7,~5\right) $ are linearly independent or dependent.	2
1627	Determine whether the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(8,~-6\right) $ are linearly independent or dependent.	2
1628	Find the angle between vectors $ \left(-4,~3\right)$ and $\left(8,~-6\right)$.	2
1629	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~12\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ .	2
1630	Determine whether the vectors $ \vec{v_1} = \left(4,~4,~4\right) $, $ \vec{v_2} = \left(11,~11,~11\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent.	2
1631	Determine whether the vectors $ \vec{v_1} = \left(-1,~-4,~-7\right) $, $ \vec{v_2} = \left(3,~8,~-1\right) $ and $ \vec{v_3} = \left(2,~-6,~-59\right)$ are linearly independent or dependent.	2
1632	Find the projection of the vector $ \vec{v_1} = \left(-3,~1,~5\right) $ on the vector $ \vec{v_2} = \left(-2,~3,~8\right) $.	2
1633	Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(12,~16\right) $ .	2
1634	Find the difference of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(12,~16\right) $ .	2
1635	Find the projection of the vector $ \vec{v_1} = \left(-4,~4\right) $ on the vector $ \vec{v_2} = \left(12,~16\right) $.	2
1636	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~0\right) $ .	2
1637	Find the angle between vectors $ \left(7,~190\right)$ and $\left(3,~90\right)$.	2
1638	Find the sum of the vectors $ \vec{v_1} = \left(7,~190\right) $ and $ \vec{v_2} = \left(3,~90\right) $ .	2
1639	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~3\right) $ .	2
1640	Find the sum of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(2,~0\right) $ .	2
1641	Find the difference of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(2,~0\right) $ .	2
1642	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-5\right) $ and $ \vec{v_2} = \left(0,~9\right) $ .	2
1643	Find the angle between vectors $ \left(9,~2\right)$ and $\left(6,~3\right)$.	2
1644	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~48\right) $ .	2
1645	Find the difference of the vectors $ \vec{v_1} = \left(5,~9\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ .	2
1646	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~9\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ .	2
1647	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~13\right) $ .	2
1648	Find the difference of the vectors $ \vec{v_1} = \left(9,~-2\right) $ and $ \vec{v_2} = \left(4,~7\right) $ .	2
1649	Find the angle between vectors $ \left(-3,~8\right)$ and $\left(6,~-4\right)$.	2
1650	Find the sum of the vectors $ \vec{v_1} = \left(8,~2\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ .	2