Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6001 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~5\right) $ and $ \vec{v_2} = \left(6,~-7,~5\right) $ . | 1 |
6002 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-6,~3\right) $ . | 1 |
6003 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(-3,~\dfrac{ 6 }{ 5 },~1\right) $ . | 1 |
6004 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4,~5\right) $ and $ \vec{v_2} = \left(2,~-3,~-4\right) $ . | 1 |
6005 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-9,~10\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
6006 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~-4\right) $ . | 1 |
6007 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~4\right) $ . | 1 |
6008 | Find the projection of the vector $ \vec{v_1} = \left(2,~2\right) $ on the vector $ \vec{v_2} = \left(2,~8\right) $. | 1 |
6009 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~-2\right) $ and $ \vec{v_2} = \left(0,~4,~2\right) $ . | 1 |
6010 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-6,~4,~-1\right) $ and $ \vec{v_2} = \left(0,~-2,~-8\right) $ . | 1 |
6011 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~-2\right) $ and $ \vec{v_2} = \left(1,~-1,~0\right) $ . | 1 |
6012 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~4,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 707107 }{ 100000 },~\dfrac{ 707107 }{ 100000 },~0\right) $ . | 1 |
6013 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~4,~-1\right) $ . | 1 |
6014 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 99 }{ 50 },~-\dfrac{ 587 }{ 100 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 413 }{ 100 },~\dfrac{ 68 }{ 25 },~0\right) $ . | 1 |
6015 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(6,~-2\right) $ . | 1 |
6016 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~4,~-2\right) $ and $ \vec{v_2} = \left(1,~-1,~-2\right) $ . | 1 |
6017 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(8,~-10\right) $ . | 1 |
6018 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(4,~-8\right) $ . | 1 |
6019 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~3,~10\right) $ . | 1 |
6020 | Find the projection of the vector $ \vec{v_1} = \left(5,~1,~-3\right) $ on the vector $ \vec{v_2} = \left(4,~2,~-6\right) $. | 1 |
6021 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(4,~2,~-2\right) $ . | 1 |
6022 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3,~5\right) $ and $ \vec{v_2} = \left(-3,~-4,~-3\right) $ . | 1 |
6023 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(7,~2\right) $ . | 1 |
6024 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~7\right) $ . | 1 |
6025 | Determine whether the vectors $ \vec{v_1} = \left(1,~4,~-1\right) $, $ \vec{v_2} = \left(1,~0,~2\right) $ and $ \vec{v_3} = \left(1,~0,~4\right)$ are linearly independent or dependent. | 1 |
6026 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-34,~-2\right) $ and $ \vec{v_2} = \left(-2,~-3,~0\right) $ . | 1 |
6027 | Find the angle between vectors $ \left(3,~-1,~-2\right)$ and $\left(1,~-1,~-2\right)$. | 1 |
6028 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5,~3\right) $ . | 1 |
6029 | Find the angle between vectors $ \left(2,~1,~1\right)$ and $\left(4,~-1,~0\right)$. | 1 |
6030 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~1,~2\right) $ and $ \vec{v_2} = \left(-4,~-2,~0\right) $ . | 1 |
6031 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~-4\right) $ and $ \vec{v_2} = \left(6,~-16\right) $ . | 1 |
6032 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~7\right) $ and $ \vec{v_2} = \left(0,~3,~-4\right) $ . | 1 |
6033 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right)$ and $\left(-\dfrac{ 1 }{ 4 },~-\dfrac{ 1 }{ 4 }\right)$. | 1 |
6034 | Calculate the dot product of the vectors $ \vec{v_1} = \left(14,~-4,~8\right) $ and $ \vec{v_2} = \left(-2,~1,~4\right) $ . | 1 |
6035 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-34,~-48,~12\right) $ and $ \vec{v_2} = \left(4,~-3,~5\right) $ . | 1 |
6036 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~2\right) $ . | 1 |
6037 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-34,~-2\right) $ and $ \vec{v_2} = \left(-2,~-3,~0\right) $ . | 1 |
6038 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~5\right) $ and $ \vec{v_2} = \left(6,~-7,~-5\right) $ . | 1 |
6039 | Find the angle between vectors $ \left(-3,~-5\right)$ and $\left(-15,~9\right)$. | 1 |
6040 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5,~6\right) $ . | 1 |
6041 | Determine whether the vectors $ \vec{v_1} = \left(3,~3,~10\right) $, $ \vec{v_2} = \left(7,~5,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
6042 | Find the magnitude of the vector $ \| \vec{v} \| = \left(192,~24\right) $ . | 1 |
6043 | Find the sum of the vectors $ \vec{v_1} = \left(3,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 1 |
6044 | Find the angle between vectors $ \left(2,~4\right)$ and $\left(4,~2\right)$. | 1 |
6045 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~0,~1\right) $ . | 1 |
6046 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~1,~5\right) $ and $ \vec{v_2} = \left(2,~-1,~4\right) $ . | 1 |
6047 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 1 |
6048 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 1 |
6049 | Find the sum of the vectors $ \vec{v_1} = \left(9,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 1 |
6050 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 129 }{ 25 },~-\dfrac{ 203 }{ 50 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 361 }{ 100 },~0,~-\dfrac{ 173 }{ 100 }\right) $ . | 1 |