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
1751	Find the sum of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ .	2
1752	Find the sum of the vectors $ \vec{v_1} = \left(4,~7\right) $ and $ \vec{v_2} = \left(8,~9\right) $ .	2
1753	Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(-10,~-8\right) $ .	2
1754	Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(3,~0\right) $ .	2
1755	Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(0,~3\right) $ .	2
1756	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ .	2
1757	Find the angle between vectors $ \left(3,~4\right)$ and $\left(-2,~-1\right)$.	2
1758	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(13,~2\right) $ .	2
1759	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 39 }{ 10 },~0\right) $ .	2
1760	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 39 }{ 10 },~\dfrac{ 23 }{ 20 }\right) $ .	2
1761	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~-1,~0\right) $ .	2
1762	Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ .	2
1763	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~4\right) $ .	2
1764	Determine whether the vectors $ \vec{v_1} = \left(-0.3333,~-1.5\right) $ and $ \vec{v_2} = \left(2,~9\right) $ are linearly independent or dependent.	2
1765	Find the projection of the vector $ \vec{v_1} = \left(-0.3333,~-1.5\right) $ on the vector $ \vec{v_2} = \left(2,~9\right) $.	2
1766	Find the angle between vectors $ \left(0,~2\right)$ and $\left(2,~1\right)$.	2
1767	Find the angle between vectors $ \left(1,~2\right)$ and $\left(2,~1\right)$.	2
1768	Find the angle between vectors $ \left(3,~2\right)$ and $\left(2,~1\right)$.	2
1769	Find the angle between vectors $ \left(-7,~2\right)$ and $\left(2,~1\right)$.	2
1770	Find the angle between vectors $ \left(-5,~2\right)$ and $\left(2,~1\right)$.	2
1771	Find the angle between vectors $ \left(-2,~2\right)$ and $\left(2,~1\right)$.	2
1772	Determine whether the vectors $ \vec{v_1} = \left(5,~6\right) $ and $ \vec{v_2} = \left(10,~5\right) $ are linearly independent or dependent.	2
1773	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~6\right) $ and $ \vec{v_2} = \left(10,~5\right) $ .	2
1774	Find the angle between vectors $ \left(-4,~-3\right)$ and $\left(4,~3\right)$.	2
1775	Find the angle between vectors $ \left(-4,~-3\right)$ and $\left(3,~4\right)$.	2
1776	Determine whether the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(1,~4\right) $ are linearly independent or dependent.	2
1777	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 21 }{ 10 },~-\dfrac{ 16 }{ 5 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	2
1778	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~5\right) $ .	2
1779	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-1,~-2\right) $ .	2
1780	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~\sqrt{ 29 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	2
1781	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	2
1782	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-1\right) $ .	2
1783	Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ .	2
1784	Find the sum of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ .	2
1785	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~-2\right) $ .	2
1786	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~6\right) $ .	2
1787	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~2\right) $ .	2
1788	Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(-9,~-3\right) $ .	2
1789	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(-9,~-2\right) $ .	2
1790	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~2,~-3\right) $ .	2
1791	Find the angle between vectors $ \left(2,~-2,~2\right)$ and $\left(1,~1,~1\right)$.	2
1792	Find the angle between vectors $ \left(1,~-2,~-1\right)$ and $\left(1,~0,~-1\right)$.	2
1793	Find the difference of the vectors $ \vec{v_1} = \left(6,~6,~6\right) $ and $ \vec{v_2} = \left(1,~-1,~1\right) $ .	2
1794	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~-1\right) $ and $ \vec{v_2} = \left(1,~0,~-1\right) $ .	2
1795	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~5\right) $ .	2
1796	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-3\right) $ .	2
1797	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(4,~5\right) $ .	2
1798	Find the angle between vectors $ \left(2,~5\right)$ and $\left(4,~-3\right)$.	2
1799	Find the projection of the vector $ \vec{v_1} = \left(-2,~9\right) $ on the vector $ \vec{v_2} = \left(-1,~2\right) $.	2
1800	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~-3\right) $ .	2