Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2801 | Find the difference of the vectors $ \vec{v_1} = \left(-48,~-25,~20\right) $ and $ \vec{v_2} = \left(60,~30,~40\right) $ . | 1 |
| 2802 | Find the projection of the vector $ \vec{v_1} = \left(7,~0\right) $ on the vector $ \vec{v_2} = \left(6.9663,~0.6861\right) $. | 1 |
| 2803 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ are linearly independent or dependent. | 1 |
| 2804 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~3\right) $, $ \vec{v_2} = \left(0,~1,~4\right) $ and $ \vec{v_3} = \left(2,~-1,~1\right)$ are linearly independent or dependent. | 1 |
| 2805 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(0,~1,~4\right) $ . | 1 |
| 2806 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~3\right) $ on the vector $ \vec{v_2} = \left(0,~1,~4\right) $. | 1 |
| 2807 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(0,~1,~4\right)$. | 1 |
| 2808 | Find the difference of the vectors $ \vec{v_1} = \left(0,~4,~0\right) $ and $ \vec{v_2} = \left(2,~-4,~3\right) $ . | 1 |
| 2809 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~4,~0\right) $ . | 1 |
| 2810 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~1,~0\right) $ . | 1 |
| 2811 | Find the angle between vectors $ \left(10,~-3\right)$ and $\left(-5,~-1\right)$. | 1 |
| 2812 | Find the angle between vectors $ \left(2,~-3\right)$ and $\left(-3,~-4\right)$. | 1 |
| 2813 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ . | 1 |
| 2814 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(6,~-3\right) $ . | 1 |
| 2815 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~-1\right) $ . | 1 |
| 2816 | Find the projection of the vector $ \vec{v_1} = \left(-2,~-1\right) $ on the vector $ \vec{v_2} = \left(6,~-2\right) $. | 1 |
| 2817 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~2\right) $ . | 1 |
| 2818 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~-4\right) $ . | 1 |
| 2819 | Determine whether the vectors $ \vec{v_1} = \left(2,~3,~-4\right) $, $ \vec{v_2} = \left(-5,~2,~7\right) $ and $ \vec{v_3} = \left(-4,~7,~-5\right)$ are linearly independent or dependent. | 1 |
| 2820 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-5,~4\right) $ and $ \vec{v_2} = \left(3,~2,~0\right) $ . | 1 |
| 2821 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-5,~4\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 2822 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~-4\right) $ . | 1 |
| 2823 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2,~0\right) $ . | 1 |
| 2824 | Find the projection of the vector $ \vec{v_1} = \left(2,~3,~-1\right) $ on the vector $ \vec{v_2} = \left(1,~1,~2\right) $. | 1 |
| 2825 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~-5\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 1 |
| 2826 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(5,~3\right) $ are linearly independent or dependent. | 1 |
| 2827 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~\dfrac{ 1 }{ 2 }\right) $ . | 1 |
| 2828 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ . | 1 |
| 2829 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-24\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 1 |
| 2830 | Find the projection of the vector $ \vec{v_1} = \left(6,~-24\right) $ on the vector $ \vec{v_2} = \left(4,~1\right) $. | 1 |
| 2831 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~5\right) $ and $ \vec{v_2} = \left(9,~-5\right) $ . | 1 |
| 2832 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~2\right) $ and $ \vec{v_2} = \left(-2,~3,~4\right) $ . | 1 |
| 2833 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~2\right) $ and $ \vec{v_2} = \left(-10,~-16,~7\right) $ . | 1 |
| 2834 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(-2,~2,~4\right) $ . | 1 |
| 2835 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(-2,~2,~4\right) $ . | 1 |
| 2836 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(-14,~-10,~-2\right) $ . | 1 |
| 2837 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-6,~9\right) $ and $ \vec{v_2} = \left(-2,~2,~4\right) $ . | 1 |
| 2838 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~1,~-5\right) $ and $ \vec{v_2} = \left(-1,~-5,~4\right) $ . | 1 |
| 2839 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~3,~1\right) $ and $ \vec{v_2} = \left(-21,~17,~16\right) $ . | 1 |
| 2840 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-3,~6\right) $ . | 1 |
| 2841 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9,~-7,~1\right) $ and $ \vec{v_2} = \left(-5,~4,~7\right) $ . | 1 |
| 2842 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-53,~-68,~1\right) $ and $ \vec{v_2} = \left(1,~1,~6\right) $ . | 1 |
| 2843 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9,~-5,~7\right) $ and $ \vec{v_2} = \left(-10,~10,~6\right) $ . | 1 |
| 2844 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~3,~4\right) $ and $ \vec{v_2} = \left(1,~4,~1\right) $ . | 1 |
| 2845 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~2\right) $ and $ \vec{v_2} = \left(-13,~6,~-11\right) $ . | 1 |
| 2846 | Find the projection of the vector $ \vec{v_1} = \left(-5,~-4\right) $ on the vector $ \vec{v_2} = \left(2,~-5\right) $. | 1 |
| 2847 | Determine whether the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(16,~-18\right) $ are linearly independent or dependent. | 1 |
| 2848 | Find the angle between vectors $ \left(6,~2\right)$ and $\left(7,~0\right)$. | 1 |
| 2849 | Find the angle between vectors $ \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 3 }{ 2 }\right)$ and $\left(16,~-18\right)$. | 1 |
| 2850 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(16,~-18\right) $ . | 1 |
