Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5051 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~5\right) $ and $ \vec{v_2} = \left(8,~-4\right) $ . | 1 |
| 5052 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(-8,~6\right) $ . | 1 |
| 5053 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(9,~22\right) $ . | 1 |
| 5054 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 8 },~\dfrac{ 5 }{ 8 }\right) $ and $ \vec{v_2} = \left(4,~21\right) $ . | 1 |
| 5055 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 8 },~\dfrac{ 5 }{ 8 }\right) $ and $ \vec{v_2} = \left(4,~21\right) $ . | 1 |
| 5056 | Determine whether the vectors $ \vec{v_1} = \left(-3,~6\right) $ and $ \vec{v_2} = \left(10,~5\right) $ are linearly independent or dependent. | 1 |
| 5057 | Determine whether the vectors $ \vec{v_1} = \left(4,~9\right) $ and $ \vec{v_2} = \left(9,~4\right) $ are linearly independent or dependent. | 1 |
| 5058 | Determine whether the vectors $ \vec{v_1} = \left(4,~9\right) $ and $ \vec{v_2} = \left(4,~9\right) $ are linearly independent or dependent. | 1 |
| 5059 | Determine whether the vectors $ \vec{v_1} = \left(4,~9\right) $ and $ \vec{v_2} = \left(-4,~-9\right) $ are linearly independent or dependent. | 1 |
| 5060 | Determine whether the vectors $ \vec{v_1} = \left(4,~-6\right) $ and $ \vec{v_2} = \left(-7,~6\right) $ are linearly independent or dependent. | 1 |
| 5061 | Determine whether the vectors $ \vec{v_1} = \left(4,~-6\right) $ and $ \vec{v_2} = \left(-7,~-3\right) $ are linearly independent or dependent. | 1 |
| 5062 | Find the angle between vectors $ \left(4,~-6\right)$ and $\left(-7,~-3\right)$. | 1 |
| 5063 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-5,~1\right) $ . | 1 |
| 5064 | Find the projection of the vector $ \vec{v_1} = \left(1,~-5,~1\right) $ on the vector $ \vec{v_2} = \left(-2,~5,~5\right) $. | 1 |
| 5065 | Determine whether the vectors $ \vec{v_1} = \left(8,~-12\right) $ and $ \vec{v_2} = \left(40,~-60\right) $ are linearly independent or dependent. | 1 |
| 5066 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 7 }{ 25 },~\dfrac{ 24 }{ 25 }\right) $ . | 1 |
| 5067 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-5,~1\right) $ and $ \vec{v_2} = \left(-2,~5,~5\right) $ . | 1 |
| 5068 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-5\right) $ and $ \vec{v_2} = \left(-10,~-7\right) $ . | 1 |
| 5069 | Find the angle between vectors $ \left(2,~0\right)$ and $\left(3,~8\right)$. | 1 |
| 5070 | Find the angle between vectors $ \left(4,~0\right)$ and $\left(3,~2\right)$. | 1 |
| 5071 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 8 }{ 9 },~-\dfrac{ 14 }{ 9 }\right) $ and $ \vec{v_2} = \left(30,~135\right) $ . | 1 |
| 5072 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~9\right) $ . | 1 |
| 5073 | Find the angle between vectors $ \left(2,~1,~3\right)$ and $\left(-4,~5,~7\right)$. | 1 |
| 5074 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~3\right) $ . | 1 |
| 5075 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~9,~0\right) $ and $ \vec{v_2} = \left(8,~-1,~0\right) $ . | 1 |
| 5076 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-3\right) $ . | 1 |
| 5077 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-10,~5\right) $ and $ \vec{v_2} = \left(-9,~-10\right) $ . | 1 |
| 5078 | Determine whether the vectors $ \vec{v_1} = \left(-10,~5\right) $ and $ \vec{v_2} = \left(-9,~-10\right) $ are linearly independent or dependent. | 1 |
| 5079 | Find the sum of the vectors $ \vec{v_1} = \left(4,~7\right) $ and $ \vec{v_2} = \left(9,~0\right) $ . | 1 |
| 5080 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-4\right) $ and $ \vec{v_2} = \left(3,~-9\right) $ . | 1 |
| 5081 | Find the angle between vectors $ \left(-4,~-6\right)$ and $\left(1,~-5\right)$. | 1 |
| 5082 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0.866,~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(-0.7071,~-0.7071\right) $ . | 1 |
| 5083 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(7,~21\right) $ . | 1 |
| 5084 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~0,~0\right) $ and $ \vec{v_2} = \left(0,~5,~0\right) $ . | 1 |
| 5085 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 5 }{ 13 },~\dfrac{ 12 }{ 13 },~0\right) $ . | 1 |
| 5086 | Find the angle between vectors $ \left(3,~-4\right)$ and $\left(2,~-1\right)$. | 1 |
| 5087 | Find the projection of the vector $ \vec{v_1} = \left(-1,~1\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 1 |
| 5088 | Determine whether the vectors $ \vec{v_1} = \left(-1,~1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent. | 1 |
| 5089 | Find the angle between vectors $ \left(-1,~1\right)$ and $\left(1,~1\right)$. | 1 |
| 5090 | Find the angle between vectors $ \left(-5,~2,~0\right)$ and $\left(-1,~8,~-4\right)$. | 1 |
| 5091 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~2,~0\right) $ and $ \vec{v_2} = \left(-1,~8,~-4\right) $ . | 1 |
| 5092 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~0,~-3\right) $ and $ \vec{v_2} = \left(1,~-3,~-1\right) $ . | 1 |
| 5093 | Calculate the dot product of the vectors $ \vec{v_1} = \left(45,~45,~45\right) $ and $ \vec{v_2} = \left(9,~9,~9\right) $ . | 1 |
| 5094 | Calculate the dot product of the vectors $ \vec{v_1} = \left(18,~18,~18\right) $ and $ \vec{v_2} = \left(36,~36,~36\right) $ . | 1 |
| 5095 | Calculate the dot product of the vectors $ \vec{v_1} = \left(18,~18,~18\right) $ and $ \vec{v_2} = \left(90,~90,~90\right) $ . | 1 |
| 5096 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(90,~90,~90\right) $ . | 1 |
| 5097 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~1\right) $ and $ \vec{v_2} = \left(-1,~1,~1\right) $ . | 1 |
| 5098 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2,~1\right) $ and $ \vec{v_2} = \left(-2,~1,~1\right) $ . | 1 |
| 5099 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~1\right) $ and $ \vec{v_2} = \left(-2,~1,~1\right) $ . | 1 |
| 5100 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~1,~1\right) $ . | 1 |
