Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5801 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~0\right) $ and $ \vec{v_2} = \left(-3,~-1,~0\right) $ . | 1 |
5802 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(-3,~-1\right) $ . | 1 |
5803 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~5,~-8\right) $ and $ \vec{v_2} = \left(2,~7,~0\right) $ . | 1 |
5804 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(3,~1,~-1\right) $ . | 1 |
5805 | Find the projection of the vector $ \vec{v_1} = \left(-2,~10,~10\right) $ on the vector $ \vec{v_2} = \left(-1,~1,~2\right) $. | 1 |
5806 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 69503 }{ 100000 },~0.0652,~\dfrac{ 30519 }{ 3125 }\right) $ . | 1 |
5807 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~11\right) $ . | 1 |
5808 | Find the angle between vectors $ \left(-4,~-1,~0\right)$ and $\left(1,~3,~-2\right)$. | 1 |
5809 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~6,~4\right) $ . | 1 |
5810 | Determine whether the vectors $ \vec{v_1} = \left(-1,~5,~0\right) $, $ \vec{v_2} = \left(-2,~2,~2\right) $ and $ \vec{v_3} = \left(10,~-26,~-6\right)$ are linearly independent or dependent. | 1 |
5811 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~6,~-5\right) $ and $ \vec{v_2} = \left(3,~-4,~8\right) $ . | 1 |
5812 | Find the angle between vectors $ \left(6,~11\right)$ and $\left(3,~-4\right)$. | 1 |
5813 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0,~-1\right) $ and $ \vec{v_2} = \left(-7,~3,~2\right) $ . | 1 |
5814 | Find the projection of the vector $ \vec{v_1} = \left(0,~1,~1\right) $ on the vector $ \vec{v_2} = \left(2,~33,~-1\right) $. | 1 |
5815 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~3\right) $ . | 1 |
5816 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9,~8,~-10\right) $ and $ \vec{v_2} = \left(4,~8,~-6\right) $ . | 1 |
5817 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2,~2\right) $ . | 1 |
5818 | Find the magnitude of the vector $ \| \vec{v} \| = \left(34,~90\right) $ . | 1 |
5819 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 10 },~-\dfrac{ 2 }{ 5 },~0\right) $ and $ \vec{v_2} = \left(0,~0,~\dfrac{ 1 }{ 10 }\right) $ . | 1 |
5820 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-5,~2\right) $ and $ \vec{v_2} = \left(-3,~-8,~8\right) $ . | 1 |
5821 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-3,~-10\right) $ . | 1 |
5822 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~3,~0\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
5823 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~11\right) $ . | 1 |
5824 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
5825 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~1\right) $ on the vector $ \vec{v_2} = \left(3,~3,~-2\right) $. | 1 |
5826 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~3,~-2\right) $ . | 1 |
5827 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
5828 | Find the projection of the vector $ \vec{v_1} = \left(4,~6,~4\right) $ on the vector $ \vec{v_2} = \left(1,~4,~8\right) $. | 1 |
5829 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-1\right) $ and $ \vec{v_2} = \left(-1,~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
5830 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~2\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 1 |
5831 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3 \sqrt{ 3 },~3\right) $ . | 1 |
5832 | Find the angle between vectors $ \left(3,~7\right)$ and $\left(1,~8\right)$. | 1 |
5833 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~-2\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
5834 | Find the angle between vectors $ \left(-12,~-4\right)$ and $\left(7,~10\right)$. | 1 |
5835 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 3 },~-\dfrac{ 1 }{ 3 },~-\dfrac{ 2 }{ 3 }\right) $, $ \vec{v_2} = \left(\dfrac{ 2 }{ 3 },~\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 11 }}{ 6 }\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
5836 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 1 |
5837 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~4,~-1\right) $ and $ \vec{v_2} = \left(32,~14,~40\right) $ . | 1 |
5838 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~2\right) $ and $ \vec{v_2} = \left(-1,~-4,~1\right) $ . | 1 |
5839 | Determine whether the vectors $ \vec{v_1} = \left(4,~-4,~8\right) $, $ \vec{v_2} = \left(5,~3,~26\right) $ and $ \vec{v_3} = \left(-4,~3,~-10\right)$ are linearly independent or dependent. | 1 |
5840 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~-10,~2\right) $ and $ \vec{v_2} = \left(7,~2,~8\right) $ . | 1 |
5841 | Find the difference of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-3,~-10\right) $ . | 1 |
5842 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(0,~3,~-2\right) $ . | 1 |
5843 | Find the sum of the vectors $ \vec{v_1} = \left(8,~5\right) $ and $ \vec{v_2} = \left(-9,~-5\right) $ . | 1 |
5844 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0,~1\right) $ and $ \vec{v_2} = \left(3,~0,~0\right) $ . | 1 |
5845 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~4\right) $, $ \vec{v_2} = \left(-\dfrac{ 1 }{ 2 },~-1,~-2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
5846 | Find the projection of the vector $ \vec{v_1} = \left(-4,~3\right) $ on the vector $ \vec{v_2} = \left(1,~2\right) $. | 1 |
5847 | Find the angle between vectors $ \left(2,~-\dfrac{ 4001 }{ 1000 }\right)$ and $\left(4,~2\right)$. | 1 |
5848 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~-2,~4\right) $ and $ \vec{v_2} = \left(0,~3,~-4\right) $ . | 1 |
5849 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
5850 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1000\right) $ and $ \vec{v_2} = \left(15,~0\right) $ . | 1 |