Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1751 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~4\right) $, $ \vec{v_2} = \left(1,~3,~5\right) $ and $ \vec{v_3} = \left(2,~1,~5\right)$ are linearly independent or dependent. | 2 |
1752 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~12\right) $ and $ \vec{v_2} = \left(9,~-1\right) $ . | 2 |
1753 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-4\right) $ . | 2 |
1754 | Find the difference of the vectors $ \vec{v_1} = \left(6,~4\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 2 |
1755 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 8 }{ 3 },~\dfrac{ 8 }{ 3 }\right) $ and $ \vec{v_2} = \left(7,~-7\right) $ . | 2 |
1756 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~10\right) $ . | 2 |
1757 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~2\right) $ . | 2 |
1758 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~-3\right) $ and $ \vec{v_2} = \left(3,~-8\right) $ . | 2 |
1759 | Find the difference of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(3,~-5\right) $ . | 2 |
1760 | Find the sum of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 2 |
1761 | Find the angle between vectors $ \left(-8,~-4,~0\right)$ and $\left(-3,~9,~7\right)$. | 2 |
1762 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-96,~-57,~-28\right) $ . | 2 |
1763 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ . | 2 |
1764 | Find the angle between vectors $ \left(-3,~-1\right)$ and $\left(-9,~-2\right)$. | 2 |
1765 | Find the angle between vectors $ \left(6,~4\right)$ and $\left(6,~0\right)$. | 2 |
1766 | Find the angle between vectors $ \left(11,~1\right)$ and $\left(3,~8\right)$. | 2 |
1767 | Find the sum of the vectors $ \vec{v_1} = \left(8,~4\right) $ and $ \vec{v_2} = \left(-9,~15\right) $ . | 2 |
1768 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~8\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ . | 2 |
1769 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-96,~-57,~-28\right) $ and $ \vec{v_2} = \left(-2,~0,~7\right) $ . | 2 |
1770 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 9 }{ 2 },~0\right) $ . | 2 |
1771 | Find the angle between vectors $ \left(-\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right)$ and $\left(\dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right)$. | 2 |
1772 | Find the angle between vectors $ \left(\dfrac{ 7361 }{ 50 },~-85\right)$ and $\left(\dfrac{ 2121 }{ 100 },~\dfrac{ 2121 }{ 100 }\right)$. | 2 |
1773 | Find the projection of the vector $ \vec{v_1} = \left(-\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right) $. | 2 |
1774 | Find the difference of the vectors $ \vec{v_1} = \left(-50,~90\right) $ and $ \vec{v_2} = \left(81,~-63\right) $ . | 2 |
1775 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~-4\right) $ and $ \vec{v_2} = \left(-6,~-2\right) $ . | 2 |
1776 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 2 |
1777 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~-4\right) $ . | 2 |
1778 | Find the angle between vectors $ \left(5,~-1\right)$ and $\left(3,~1\right)$. | 2 |
1779 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(-3,~9\right) $ . | 2 |
1780 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~0\right) $ and $ \vec{v_2} = \left(4,~-9\right) $ . | 2 |
1781 | Find the difference of the vectors $ \vec{v_1} = \left(-45,~81\right) $ and $ \vec{v_2} = \left(-36,~28\right) $ . | 2 |
1782 | Find the projection of the vector $ \vec{v_1} = \left(-1,~-8,~3\right) $ on the vector $ \vec{v_2} = \left(-3,~-3,~-3\right) $. | 2 |
1783 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-3\right) $ and $ \vec{v_2} = \left(-8,~2\right) $ . | 2 |
1784 | Find the sum of the vectors $ \vec{v_1} = \left(-12,~-6\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ . | 2 |
1785 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 9 }{ 2 },~\dfrac{ 16 }{ 5 }\right) $ . | 2 |
1786 | Find the difference of the vectors $ \vec{v_1} = \left(-160,~80\right) $ and $ \vec{v_2} = \left(-140,~280\right) $ . | 2 |
1787 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~2\right) $ and $ \vec{v_2} = \left(-1,~-1\right) $ . | 2 |
1788 | Find the angle between vectors $ \left(5,~3\right)$ and $\left(-2,~4\right)$. | 2 |
1789 | Find the sum of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(0,~2\right) $ . | 2 |
1790 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(8,~-4\right) $ . | 2 |
1791 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~7\right) $ . | 2 |
1792 | Find the difference of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(6,~4\right) $ . | 2 |
1793 | Find the angle between vectors $ \left(1,~1,~1\right)$ and $\left(-2,~1,~1\right)$. | 2 |
1794 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 183 }{ 10 },~\dfrac{ 21353 }{ 1000 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 60743 }{ 1000 },~\dfrac{ 1194 }{ 25 }\right) $ . | 2 |
1795 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~-4\right) $ and $ \vec{v_2} = \left(1,~-4\right) $ . | 2 |
1796 | Find the angle between vectors $ \left(5,~-2\right)$ and $\left(-7,~-3\right)$. | 2 |
1797 | Find the difference of the vectors $ \vec{v_1} = \left(-45,~81\right) $ and $ \vec{v_2} = \left(36,~-28\right) $ . | 2 |
1798 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~-3\right) $ and $ \vec{v_2} = \left(-8,~2\right) $ . | 2 |
1799 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-4\right) $ and $ \vec{v_2} = \left(1,~-4\right) $ . | 2 |
1800 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-2\right) $ . | 2 |