Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
3001 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~6\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 1 |
3002 | Determine whether the vectors $ \vec{v_1} = \left(4,~4\right) $ and $ \vec{v_2} = \left(0,~0\right) $ are linearly independent or dependent. | 1 |
3003 | Determine whether the vectors $ \vec{v_1} = \left(0.2,~0.2,~0.2\right) $, $ \vec{v_2} = \left(0.2,~0.4,~0.3\right) $ and $ \vec{v_3} = \left(0.6,~0.4,~0.5\right)$ are linearly independent or dependent. | 1 |
3004 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~1\right) $ . | 1 |
3005 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-8,~8\right) $ and $ \vec{v_2} = \left(-4,~6,~8\right) $ . | 1 |
3006 | Find the angle between vectors $ \left(-8,~\sqrt{ 7 }\right)$ and $\left(64,~36\right)$. | 1 |
3007 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~6\right) $ and $ \vec{v_2} = \left(-4,~5\right) $ . | 1 |
3008 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 1 |
3009 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-3,~0\right) $ and $ \vec{v_2} = \left(-1,~2,~-4\right) $ . | 1 |
3010 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~5\right) $ . | 1 |
3011 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~5,~9\right) $ and $ \vec{v_2} = \left(2,~5,~4\right) $ . | 1 |
3012 | Determine whether the vectors $ \vec{v_1} = \left(-4,~2,~2\right) $, $ \vec{v_2} = \left(2,~-3,~1\right) $ and $ \vec{v_3} = \left(1,~-1,~2\right)$ are linearly independent or dependent. | 1 |
3013 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~5,~3\right) $ and $ \vec{v_2} = \left(4,~1,~0\right) $ . | 1 |
3014 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(2,~6\right) $ . | 1 |
3015 | Determine whether the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(2,~8\right) $ are linearly independent or dependent. | 1 |
3016 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~1\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 1 |
3017 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(66,~12\right) $ . | 1 |
3018 | Find the projection of the vector $ \vec{v_1} = \left(5,~7,~1\right) $ on the vector $ \vec{v_2} = \left(6,~-6,~1\right) $. | 1 |
3019 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9.88,~0,~0\right) $ and $ \vec{v_2} = \left(2.1,~-2.6,~0\right) $ . | 1 |
3020 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 1 |
3021 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~-1,~-4\right) $ and $ \vec{v_2} = \left(4,~-1,~-4\right) $ . | 1 |
3022 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~-1,~4\right) $ . | 1 |
3023 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~5\right) $ and $ \vec{v_2} = \left(17,~35\right) $ . | 1 |
3024 | Calculate the cross product of the vectors $ \vec{v_1} = \left(23,~6,~0\right) $ and $ \vec{v_2} = \left(17,~5,~0\right) $ . | 1 |
3025 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-2,~5\right) $ and $ \vec{v_2} = \left(2,~1,~-3\right) $ . | 1 |
3026 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~-3\right) $ . | 1 |
3027 | Find the angle between vectors $ \left(2,~3\right)$ and $\left(2,~1\right)$. | 1 |
3028 | Find the difference of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(5,~6\right) $ . | 1 |
3029 | Find the angle between vectors $ \left(5,~4\right)$ and $\left(6,~-1\right)$. | 1 |
3030 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3130,~108\right) $ . | 1 |
3031 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(8,~-2\right) $ . | 1 |
3032 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-3,~1\right) $ and $ \vec{v_2} = \left(2,~-4,~1\right) $ . | 1 |
3033 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~2\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 1 |
3034 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(-1,~0\right) $ . | 1 |
3035 | Find the sum of the vectors $ \vec{v_1} = \left(6,~3\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
3036 | | 1 |
3037 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 1 |
3038 | Find the angle between vectors $ \left(0.1534,~-0.8874,~0.4347\right)$ and $\left(-0.3783,~-0.5898,~0.7134\right)$. | 1 |
3039 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 1 |
3040 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-3 \sqrt{ 3 }\right) $ . | 1 |
3041 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-6,~0\right) $ and $ \vec{v_2} = \left(-3,~6,~-12\right) $ . | 1 |
3042 | Find the projection of the vector $ \vec{v_1} = \left(3,~5\right) $ on the vector $ \vec{v_2} = \left(7,~2\right) $. | 1 |
3043 | Find the angle between vectors $ \left(1,~-4\right)$ and $\left(-3,~-2\right)$. | 1 |
3044 | Find the difference of the vectors $ \vec{v_1} = \left(10,~10\right) $ and $ \vec{v_2} = \left(15,~20\right) $ . | 1 |
3045 | Find the angle between vectors $ \left(0,~-5,~7\right)$ and $\left(-5,~1,~5\right)$. | 1 |
3046 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~5,~3\right) $ and $ \vec{v_2} = \left(-8,~-1,~0\right) $ . | 1 |
3047 | Find the projection of the vector $ \vec{v_1} = \left(2,~-1,~3\right) $ on the vector $ \vec{v_2} = \left(-4,~2,~1\right) $. | 1 |
3048 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(2,~-1,~6\right) $ . | 1 |
3049 | Find the angle between vectors $ \left(3,~-5,~-7\right)$ and $\left(1,~-3,~2\right)$. | 1 |
3050 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(-4,~0\right) $ . | 1 |