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
1651	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~2\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ .	2
1652	Find the sum of the vectors $ \vec{v_1} = \left(-6,~-7\right) $ and $ \vec{v_2} = \left(3,~-3\right) $ .	2
1653	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~4\right) $ .	2
1654	Find the angle between vectors $ \left(6,~4\right)$ and $\left(6,~0\right)$.	2
1655	Find the difference of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(6,~4\right) $ .	2
1656	Find the difference of the vectors $ \vec{v_1} = \left(-3,~-2\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ .	2
1657	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-1\right) $ .	2
1658	Find the difference of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ .	2
1659	Find the difference of the vectors $ \vec{v_1} = \left(-6,~-6\right) $ and $ \vec{v_2} = \left(-8,~0\right) $ .	2
1660	Find the sum of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(8,~-4\right) $ .	2
1661	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~-3\right) $ .	2
1662	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 61 }{ 10 },~\dfrac{ 17 }{ 2 }\right) $ .	2
1663	Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 61 }{ 10 },~\dfrac{ 17 }{ 2 }\right) $ and $ \vec{v_2} = \left(-5,~\dfrac{ 9 }{ 2 }\right) $ .	2
1664	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(2,~5\right) $ .	2
1665	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~3\right) $ .	2
1666	Find the sum of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ .	2
1667	Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-3\right) $ and $ \vec{v_2} = \left(-8,~2\right) $ .	2
1668	Find the sum of the vectors $ \vec{v_1} = \left(-8,~-3\right) $ and $ \vec{v_2} = \left(-8,~2\right) $ .	2
1669	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 9 }{ 7 },~0\right) $ .	2
1670	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~-3\right) $ .	2
1671	Find the difference of the vectors $ \vec{v_1} = \left(-4,~-6\right) $ and $ \vec{v_2} = \left(9,~-3\right) $ .	2
1672	Find the sum of the vectors $ \vec{v_1} = \left(12,~12\right) $ and $ \vec{v_2} = \left(-5,~\dfrac{ 9 }{ 2 }\right) $ .	2
1673	Find the difference of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(14,~18\right) $ .	2
1674	Find the sum of the vectors $ \vec{v_1} = \left(-6,~-15\right) $ and $ \vec{v_2} = \left(14,~8\right) $ .	2
1675	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~-2\right) $ .	2
1676	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~6\right) $ and $ \vec{v_2} = \left(10,~1\right) $ .	2
1677	Find the angle between vectors $ \left(4,~6\right)$ and $\left(10,~1\right)$.	2
1678	Find the angle between vectors $ \left(\sqrt{ 7 },~\sqrt{ 8 }\right)$ and $\left(\sqrt{ 8 },~\sqrt{ 7 }\right)$.	2
1679	Calculate the dot product of the vectors $ \vec{v_1} = \left(25,~20\right) $ and $ \vec{v_2} = \left(6,~-6\right) $ .	2
1680	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ .	2
1681	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~-40,~0\right) $ .	2
1682	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(7,~5\right) $ .	2
1683	Find the sum of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ .	2
1684	Find the sum of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ .	2
1685	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~-5\right) $ .	2
1686	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ .	2
1687	Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~0,~0\right) $ and $ \vec{v_2} = \left(-7,~4,~0\right) $ .	2
1688	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~6\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ .	2
1689	Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~6,~0\right) $ and $ \vec{v_2} = \left(-7,~4,~0\right) $ .	2
1690	Find the angle between vectors $ \left(11,~1\right)$ and $\left(3,~8\right)$.	2
1691	Find the angle between vectors $ \left(3,~1\right)$ and $\left(-4,~-3\right)$.	2
1692	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(9,~\sqrt{ 19 }\right) $ .	2
1693	Find the angle between vectors $ \left(3,~4\right)$ and $\left(3,~-4\right)$.	2
1694	Find the projection of the vector $ \vec{v_1} = \left(1,~3\right) $ on the vector $ \vec{v_2} = \left(3,~-3\right) $.	2
1695	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-3\right) $ and $ \vec{v_2} = \left(4,~0\right) $ .	2
1696	Find the difference of the vectors $ \vec{v_1} = \left(55,~-10\right) $ and $ \vec{v_2} = \left(30,~12\right) $ .	2
1697	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~6\right) $ .	2
1698	Calculate the dot product of the vectors $ \vec{v_1} = \left(100,~200,~-50\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ .	2
1699	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(7,~4\right) $ .	2
1700	Find the difference of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(0,~8\right) $ .	2