Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3001 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-3,~4\right) $ and $ \vec{v_2} = \left(1,~5,~0\right) $ . | 1 |
| 3002 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~5\right) $ and $ \vec{v_2} = \left(-9,~-2\right) $ . | 1 |
| 3003 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~1\right) $ . | 1 |
| 3004 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 1 |
| 3005 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 1 |
| 3006 | Find the difference of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 1 |
| 3007 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ . | 1 |
| 3008 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ . | 1 |
| 3009 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(3,~-10\right) $ . | 1 |
| 3010 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(1,~3,~-5\right) $ . | 1 |
| 3011 | Find the angle between vectors $ \left(3,~5,~-1\right)$ and $\left(9,~8,~5\right)$. | 1 |
| 3012 | Find the angle between vectors $ \left(6,~6,~-3\right)$ and $\left(6,~3,~6\right)$. | 1 |
| 3013 | Find the sum of the vectors $ \vec{v_1} = \left(6,~1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
| 3014 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-5\right) $ . | 1 |
| 3015 | Determine whether the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(12,~15\right) $ are linearly independent or dependent. | 1 |
| 3016 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 51 }{ 5 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 23 }{ 2 },~33\right) $ . | 1 |
| 3017 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2,~0\right) $ . | 1 |
| 3018 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~0\right) $ and $ \vec{v_2} = \left(1,~-2,~-1\right) $ . | 1 |
| 3019 | Calculate the dot product of the vectors $ \vec{v_1} = \left(30,~16,~23\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 50 },~0,~0\right) $ . | 1 |
| 3020 | Find the difference of the vectors $ \vec{v_1} = \left(7,~-6\right) $ and $ \vec{v_2} = \left(16,~22\right) $ . | 1 |
| 3021 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-4,~0\right) $ and $ \vec{v_2} = \left(1,~5,~3\right) $ . | 1 |
| 3022 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-4,~-1\right) $ and $ \vec{v_2} = \left(-3,~9,~3\right) $ . | 1 |
| 3023 | Find the difference of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ . | 1 |
| 3024 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
| 3025 | Find the difference of the vectors $ \vec{v_1} = \left(-9,~4\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
| 3026 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-6,~0\right) $ . | 1 |
| 3027 | Find the angle between vectors $ \left(-4,~-4,~3\right)$ and $\left(1,~3,~-2\right)$. | 1 |
| 3028 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~6\right) $ . | 1 |
| 3029 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-10\right) $ and $ \vec{v_2} = \left(12,~-4\right) $ . | 1 |
| 3030 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(1,~6\right) $ . | 1 |
| 3031 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
| 3032 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~1\right) $ . | 1 |
| 3033 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 1 |
| 3034 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 1 |
| 3035 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~1\right) $ on the vector $ \vec{v_2} = \left(0,~2,~1\right) $. | 1 |
| 3036 | Find the angle between vectors $ \left(3,~-5\right)$ and $\left(6,~10\right)$. | 1 |
| 3037 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2 \sqrt{ 3 }\right) $ . | 1 |
| 3038 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~10\right) $ . | 1 |
| 3039 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~6,~8\right) $ . | 1 |
| 3040 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3\right) $ . | 1 |
| 3041 | Find the sum of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(7,~-5\right) $ . | 1 |
| 3042 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~12\right) $ and $ \vec{v_2} = \left(9,~-1\right) $ . | 1 |
| 3043 | Find the angle between vectors $ \left(-5,~12\right)$ and $\left(9,~-1\right)$. | 1 |
| 3044 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 3045 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(1,~-1,~2\right) $ . | 1 |
| 3046 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(1,~2,~0\right) $ . | 1 |
| 3047 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 1 |
| 3048 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1,~-2\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 1 |
| 3049 | Find the projection of the vector $ \vec{v_1} = \left(-2,~4\right) $ on the vector $ \vec{v_2} = \left(-2,~1\right) $. | 1 |
| 3050 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~4,~1\right) $ and $ \vec{v_2} = \left(2,~0,~0\right) $ . | 1 |
