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
1701	Find the sum of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(1,~3\right) $ .	2
1702	Find the sum of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(3,~3\right) $ .	2
1703	Find the angle between vectors $ \left(2 \sqrt{ 3 },~\sqrt{ 3 },~-1\right)$ and $\left(1,~-2,~2\right)$.	2
1704	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(9,~12\right) $ .	2
1705	Find the angle between vectors $ \left(5,~-1\right)$ and $\left(3,~2\right)$.	2
1706	Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 5387 }{ 125 },~\dfrac{ 68951 }{ 1250 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 10363 }{ 125 },~-\dfrac{ 55919 }{ 1000 }\right) $ .	2
1707	Find the sum of the vectors $ \vec{v_1} = \left(16,~0\right) $ and $ \vec{v_2} = \left(0,~-14\right) $ .	2
1708	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~4\right) $ .	2
1709	Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(1,~3\right) $ .	2
1710	Find the difference of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(8,~-6\right) $ .	2
1711	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~1\right) $ .	2
1712	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-1\right) $ and $ \vec{v_2} = \left(4,~-8\right) $ .	2
1713	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 83 }{ 10 },~3\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 5 },~\dfrac{ 34 }{ 5 }\right) $ .	2
1714	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 83 }{ 10 },~3\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 5 },~\dfrac{ 34 }{ 5 }\right) $ .	2
1715	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 97 }{ 10 },~\dfrac{ 49 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 5 },~\dfrac{ 34 }{ 5 }\right) $ .	2
1716	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ .	2
1717	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ .	2
1718	Determine whether the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ are linearly independent or dependent.	2
1719	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-2\right) $ .	2
1720	Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~8,~10\right) $ and $ \vec{v_2} = \left(4,~2,~-6\right) $ .	2
1721	Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-6\right) $ and $ \vec{v_2} = \left(2,~-1,~3\right) $ .	2
1722	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~1,~-3\right) $ and $ \vec{v_2} = \left(2,~-1,~3\right) $ .	2
1723	Find the sum of the vectors $ \vec{v_1} = \left(1,~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(2,~5\right) $ .	2
1724	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~\dfrac{ 1 }{ 2 }\right) $ .	2
1725	Find the difference of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(7,~-15\right) $ .	2
1726	Find the sum of the vectors $ \vec{v_1} = \left(-7,~-1,~2\right) $ and $ \vec{v_2} = \left(-1,~1,~5\right) $ .	2
1727	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~-4\right) $ and $ \vec{v_2} = \left(-3,~2,~3\right) $ .	2
1728	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~5\right) $ .	2
1729	Find the sum of the vectors $ \vec{v_1} = \left(-7,~0\right) $ and $ \vec{v_2} = \left(5,~5\right) $ .	2
1730	Find the difference of the vectors $ \vec{v_1} = \left(-7,~0\right) $ and $ \vec{v_2} = \left(5,~5\right) $ .	2
1731	Find the angle between vectors $ \left(-7,~0\right)$ and $\left(8,~-1\right)$.	2
1732	Find the projection of the vector $ \vec{v_1} = \left(-7,~0\right) $ on the vector $ \vec{v_2} = \left(8,~-1\right) $.	2
1733	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-7,~0\right) $ .	2
1734	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~2\right) $ .	2
1735	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ .	2
1736	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-5\right) $ .	2
1737	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~0\right) $ .	2
1738	Find the projection of the vector $ \vec{v_1} = \left(1,~0\right) $ on the vector $ \vec{v_2} = \left(2,~1\right) $.	2
1739	Find the projection of the vector $ \vec{v_1} = \left(2,~0\right) $ on the vector $ \vec{v_2} = \left(2,~1\right) $.	2
1740	Find the projection of the vector $ \vec{v_1} = \left(2,~0\right) $ on the vector $ \vec{v_2} = \left(4,~2\right) $.	2
1741	Find the projection of the vector $ \vec{v_1} = \left(2,~0\right) $ on the vector $ \vec{v_2} = \left(6,~3\right) $.	2
1742	Find the projection of the vector $ \vec{v_1} = \left(0,~1\right) $ on the vector $ \vec{v_2} = \left(2,~1\right) $.	2
1743	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~8\right) $ .	2
1744	Find the sum of the vectors $ \vec{v_1} = \left(-2,~8\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ .	2
1745	Find the angle between vectors $ \left(-2,~8\right)$ and $\left(4,~-3\right)$.	2
1746	Determine whether the vectors $ \vec{v_1} = \left(-\dfrac{ 27 }{ 100 },~-\dfrac{ 9 }{ 25 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 27 }{ 100 },~-\dfrac{ 9 }{ 25 }\right) $ are linearly independent or dependent.	2
1747	Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(2,~5\right) $.	2
1748	Find the sum of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ .	2
1749	Find the sum of the vectors $ \vec{v_1} = \left(1,~9\right) $ and $ \vec{v_2} = \left(4,~3\right) $ .	2
1750	Find the sum of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ .	2