Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6051 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 10 },~\dfrac{ 22 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 11 }{ 10 },~\dfrac{ 5 }{ 2 }\right) $ . | 1 |
6052 | Find the angle between vectors $ \left(2,~-34,~-2\right)$ and $\left(-2,~-3,~0\right)$. | 1 |
6053 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $. | 1 |
6054 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2,~0\right) $ . | 1 |
6055 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~5\right) $ and $ \vec{v_2} = \left(-1,~-2,~0\right) $ . | 1 |
6056 | Find the angle between vectors $ \left(2,~4\right)$ and $\left(-1,~8\right)$. | 1 |
6057 | Find the sum of the vectors $ \vec{v_1} = \left(0,~6\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ . | 1 |
6058 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-12,~-15\right) $ . | 1 |
6059 | Determine whether the vectors $ \vec{v_1} = \left(-3,~-4\right) $ and $ \vec{v_2} = \left(6,~-16\right) $ are linearly independent or dependent. | 1 |
6060 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~0\right) $ . | 1 |
6061 | Find the difference of the vectors $ \vec{v_1} = \left(3,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 1 |
6062 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~\dfrac{ 1 }{ 2 }\right) $ . | 1 |
6063 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 1 |
6064 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 1 |
6065 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(-5,~5,~0\right) $ . | 1 |
6066 | Find the angle between vectors $ \left(0,~-1\right)$ and $\left(-6,~0\right)$. | 1 |
6067 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~3\right) $ . | 1 |
6068 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-5\right) $ . | 1 |
6069 | Find the angle between vectors $ \left(2,~0\right)$ and $\left(0,~-7\right)$. | 1 |
6070 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ . | 1 |
6071 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 1 |
6072 | Find the magnitude of the vector $ \| \vec{v} \| = \left(25,~23\right) $ . | 1 |
6073 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~41\right) $ . | 1 |
6074 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(0,~5\right) $ . | 1 |
6075 | Find the angle between vectors $ \left(2,~7,~5\right)$ and $\left(2,~7,~0\right)$. | 1 |
6076 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 1 |
6077 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~3,~-8\right) $ . | 1 |
6078 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~4,~-2\right) $ and $ \vec{v_2} = \left(3,~-5,~-9\right) $ . | 1 |
6079 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-12,~-15\right) $ . | 1 |
6080 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
6081 | Find the angle between vectors $ \left(2,~1,~0\right)$ and $\left(3,~-1,~1\right)$. | 1 |
6082 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(4,~2\right)$. | 1 |
6083 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~7\right) $ and $ \vec{v_2} = \left(-37,~8,~6\right) $ . | 1 |
6084 | Find the difference of the vectors $ \vec{v_1} = \left(1,~0,~8\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
6085 | Find the projection of the vector $ \vec{v_1} = \left(6,~-10\right) $ on the vector $ \vec{v_2} = \left(-1,~1\right) $. | 1 |
6086 | Find the angle between vectors $ \left(-1,~-1,~1\right)$ and $\left(-1,~-1,~2\right)$. | 1 |
6087 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-4\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 1 |
6088 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~8,~-2\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 1 |
6089 | Find the difference 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 |
6090 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 1 |
6091 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2,~1\right) $ . | 1 |
6092 | Find the angle between vectors $ \left(1,~2,~5\right)$ and $\left(-1,~-2,~0\right)$. | 1 |
6093 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-8,~5\right) $ and $ \vec{v_2} = \left(2,~-1,~7\right) $ . | 1 |
6094 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(8,~-6\right) $ . | 1 |
6095 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~7\right) $ and $ \vec{v_2} = \left(2,~4,~7\right) $ . | 1 |
6096 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~0.3333\right) $ and $ \vec{v_2} = \left(6,~-3,~-6\right) $ . | 1 |
6097 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right)$ and $\left(-\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right)$. | 1 |
6098 | Find the angle between vectors $ \left(2,~0,~-1\right)$ and $\left(2,~-1,~2\right)$. | 1 |
6099 | Find the sum of the vectors $ \vec{v_1} = \left(-48,~-25,~20\right) $ and $ \vec{v_2} = \left(60,~30,~40\right) $ . | 1 |
6100 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~-1\right) $ and $ \vec{v_2} = \left(2,~1,~-3\right) $ . | 1 |