Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1701 | Find the angle between vectors $ \left(3,~5\right)$ and $\left(0,~-4\right)$. | 2 |
1702 | Find the difference of the vectors $ \vec{v_1} = \left(220,~30\right) $ and $ \vec{v_2} = \left(-190,~285.27\right) $ . | 2 |
1703 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 2 |
1704 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-7\right) $ . | 2 |
1705 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~-2\right) $ . | 2 |
1706 | Find the projection of the vector $ \vec{v_1} = \left(0,~-2,~-1\right) $ on the vector $ \vec{v_2} = \left(-64,~-2,~30\right) $. | 2 |
1707 | Find the angle between vectors $ \left(3,~-4\right)$ and $\left(1,~0\right)$. | 2 |
1708 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~5\right) $ . | 2 |
1709 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(-7,~6,~0\right) $ . | 2 |
1710 | 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 |
1711 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(7,~0\right) $ . | 2 |
1712 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~15\right) $ . | 2 |
1713 | Find the difference of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 2 |
1714 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ . | 2 |
1715 | Find the projection of the vector $ \vec{v_1} = \left(3,~5\right) $ on the vector $ \vec{v_2} = \left(0,~-4\right) $. | 2 |
1716 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 2 |
1717 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 2 |
1718 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(7,~6\right) $ . | 2 |
1719 | Find the angle between vectors $ \left(-9,~-2\right)$ and $\left(-5,~-7\right)$. | 2 |
1720 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 2 |
1721 | Find the sum of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(2,~-7\right) $ . | 2 |
1722 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~5\right) $ . | 2 |
1723 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ . | 2 |
1724 | Determine whether the vectors $ \vec{v_1} = \left(-5,~12\right) $ and $ \vec{v_2} = \left(9,~-1\right) $ are linearly independent or dependent. | 2 |
1725 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(-2,~6,~0\right) $ . | 2 |
1726 | Find the angle between vectors $ \left(\sqrt{ 7 },~\sqrt{ 8 }\right)$ and $\left(\sqrt{ 8 },~\sqrt{ 7 }\right)$. | 2 |
1727 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 2 |
1728 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1\right) $ . | 2 |
1729 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-8\right) $ and $ \vec{v_2} = \left(-5,~-3\right) $ . | 2 |
1730 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-8\right) $ . | 2 |
1731 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 5017 }{ 10 },~\dfrac{ 34 }{ 5 }\right) $ . | 2 |
1732 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 2 |
1733 | Determine whether the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(4,~-2\right) $ are linearly independent or dependent. | 2 |
1734 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~3\right) $ . | 2 |
1735 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~-5\right) $ . | 2 |
1736 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~4\right) $ . | 2 |
1737 | Find the sum of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(8,~0\right) $ . | 2 |
1738 | Find the projection of the vector $ \vec{v_1} = \left(2,~4\right) $ on the vector $ \vec{v_2} = \left(1,~-1\right) $. | 2 |
1739 | Find the angle between vectors $ \left(\dfrac{ 8 }{ 3 },~\dfrac{ 8 }{ 3 }\right)$ and $\left(7,~-7\right)$. | 2 |
1740 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 2 |
1741 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ . | 2 |
1742 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~3\right) $ . | 2 |
1743 | Find the difference of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 2 |
1744 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~12\right) $ . | 2 |
1745 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 2 |
1746 | Find the angle between vectors $ \left(2,~1,~-1\right)$ and $\left(-1,~-2,~5\right)$. | 2 |
1747 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~5\right) $ . | 2 |
1748 | Find the difference of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(8,~0\right) $ . | 2 |
1749 | Find the angle between vectors $ \left(3,~-8,~6\right)$ and $\left(-5,~4,~9\right)$. | 2 |
1750 | Find the angle between vectors $ \left(4,~3\right)$ and $\left(3,~-4\right)$. | 2 |