Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 51 | Find the projection of the vector $ \vec{v_1} = \left(2,~-6\right) $ on the vector $ \vec{v_2} = \left(-\dfrac{ 1 }{ 3 },~\dfrac{ 3 }{ 5 }\right) $. | 5 |
| 52 | Find the difference of the vectors $ \vec{v_1} = \left(9,~5\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 5 |
| 53 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 5 |
| 54 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 5 |
| 55 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-15,~-45\right) $ . | 5 |
| 56 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-12\right) $ . | 5 |
| 57 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 21 }{ 10 },~-\dfrac{ 16 }{ 5 }\right) $ . | 5 |
| 58 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-2\right) $ . | 5 |
| 59 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~2\right) $ . | 5 |
| 60 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 5 |
| 61 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-9\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ . | 5 |
| 62 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 5 |
| 63 | Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(10,~5\right) $. | 5 |
| 64 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~9\right) $ . | 5 |
| 65 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~3\right) $ . | 5 |
| 66 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(4,~5,~6\right) $ . | 5 |
| 67 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 4 },~2\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 5 |
| 68 | Find the angle between vectors $ \left(5,~-3\right)$ and $\left(-8,~8\right)$. | 5 |
| 69 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~3\right) $ . | 5 |
| 70 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~12\right) $ . | 5 |
| 71 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 5 |
| 72 | Find the angle between vectors $ \left(4,~3\right)$ and $\left(2,~3\right)$. | 5 |
| 73 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(5,~29\right) $ . | 5 |
| 74 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-3\right) $ . | 5 |
| 75 | Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 5 |
| 76 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(1,~-1\right)$. | 5 |
| 77 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 5 |
| 78 | Find the difference of the vectors $ \vec{v_1} = \left(7,~1\right) $ and $ \vec{v_2} = \left(5,~5\right) $ . | 5 |
| 79 | Find the difference of the vectors $ \vec{v_1} = \left(10,~-1\right) $ and $ \vec{v_2} = \left(10,~-4\right) $ . | 5 |
| 80 | Find the angle between vectors $ \left(-78,~44\right)$ and $\left(87,~80\right)$. | 5 |
| 81 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 5 |
| 82 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~3\right) $ . | 5 |
| 83 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(28,~-49\right) $ . | 5 |
| 84 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 5 |
| 85 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 4 |
| 86 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-1\right) $ and $ \vec{v_2} = \left(5,~7\right) $ . | 4 |
| 87 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-10,~2\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 4 |
| 88 | Find the angle between vectors $ \left(-7,~-5\right)$ and $\left(2,~-8\right)$. | 4 |
| 89 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-3,~-3\right) $ . | 4 |
| 90 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 4 |
| 91 | Find the sum of the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 4 |
| 92 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~3\right) $ and $ \vec{v_2} = \left(-3,~6\right) $ . | 4 |
| 93 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~-3\right) $ and $ \vec{v_2} = \left(3,~-8\right) $ . | 4 |
| 94 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 4 |
| 95 | Find the projection of the vector $ \vec{v_1} = \left(8,~5\right) $ on the vector $ \vec{v_2} = \left(-9,~-2\right) $. | 4 |
| 96 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 4 |
| 97 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 4 |
| 98 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 4 |
| 99 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 4 |
| 100 | Find the sum of the vectors $ \vec{v_1} = \left(11,~2\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 4 |
