Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6051 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~2,~2\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 6052 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~10,~-6\right) $ . | 1 |
| 6053 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~2,~0\right) $ . | 1 |
| 6054 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~3,~5\right) $ and $ \vec{v_2} = \left(1,~0,~-2\right) $ . | 1 |
| 6055 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-3,~6,~-15\right) $ . | 1 |
| 6056 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~4\right) $ and $ \vec{v_2} = \left(1,~1,~4\right) $ . | 1 |
| 6057 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(1,~-2,~3\right) $ . | 1 |
| 6058 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-3,~3,~2\right) $ . | 1 |
| 6059 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9,~-6,~3\right) $ and $ \vec{v_2} = \left(-4,~4,~2\right) $ . | 1 |
| 6060 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~1,~2\right) $ . | 1 |
| 6061 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~-2,~1\right) $ and $ \vec{v_2} = \left(-6,~4,~9\right) $ . | 1 |
| 6062 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-8,~8\right) $ and $ \vec{v_2} = \left(-4,~6,~8\right) $ . | 1 |
| 6063 | Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(-4,~12\right) $. | 1 |
| 6064 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
| 6065 | Find the angle between vectors $ \left(-4,~-3\right)$ and $\left(-1,~5\right)$. | 1 |
| 6066 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~8\right) $ and $ \vec{v_2} = \left(2,~7\right) $ . | 1 |
| 6067 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(24,~3\right) $ . | 1 |
| 6068 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(24,~3\right) $ . | 1 |
| 6069 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~4\right) $ . | 1 |
| 6070 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
| 6071 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 13 }{ 10 },~\dfrac{ 481 }{ 100 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 37 }{ 5 },~2\right) $ . | 1 |
| 6072 | Find the magnitude of the vector $ \| \vec{v} \| = \left(32,~-21\right) $ . | 1 |
| 6073 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 3 },~-\dfrac{ 1 }{ 3 },~-\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 2 }{ 3 },~\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 11 }}{ 6 }\right) $ . | 1 |
| 6074 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-45,~35\right) $ . | 1 |
| 6075 | Determine whether the vectors $ \vec{v_1} = \left(-27,~-21\right) $ and $ \vec{v_2} = \left(-9,~-7\right) $ are linearly independent or dependent. | 1 |
| 6076 | Find the difference of the vectors $ \vec{v_1} = \left(-18,~14\right) $ and $ \vec{v_2} = \left(-50,~30\right) $ . | 1 |
| 6077 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~2\right) $ and $ \vec{v_2} = \left(3,~1,~2\right) $ . | 1 |
| 6078 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 1 |
| 6079 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-7\right) $ . | 1 |
| 6080 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(3,~6\right) $ . | 1 |
| 6081 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~9\right) $ and $ \vec{v_2} = \left(20,~-15\right) $ . | 1 |
| 6082 | Find the difference of the vectors $ \vec{v_1} = \left(8,~-6\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
| 6083 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 1 |
| 6084 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~0,~0\right) $ . | 1 |
| 6085 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(6,~2\right) $ . | 1 |
| 6086 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~9,~4\right) $ and $ \vec{v_2} = \left(5,~-5,~-8\right) $ . | 1 |
| 6087 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 1 |
| 6088 | Determine whether the vectors $ \vec{v_1} = \left(8,~20\right) $ and $ \vec{v_2} = \left(-2,~-5\right) $ are linearly independent or dependent. | 1 |
| 6089 | Find the angle between vectors $ \left(-4,~-5\right)$ and $\left(1,~3\right)$. | 1 |
| 6090 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-10,~7\right) $ . | 1 |
| 6091 | Find the angle between vectors $ \left(4,~7\right)$ and $\left(8,~3\right)$. | 1 |
| 6092 | Determine whether the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(9,~-7\right) $ are linearly independent or dependent. | 1 |
| 6093 | Determine whether the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(-9,~7\right) $ are linearly independent or dependent. | 1 |
| 6094 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-6\right) $ . | 1 |
| 6095 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~4,~-1\right) $ . | 1 |
| 6096 | 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 |
| 6097 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-1\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 1 |
| 6098 | Find the angle between vectors $ \left(-5,~7\right)$ and $\left(-6,~-4\right)$. | 1 |
| 6099 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~5,~-1\right) $ . | 1 |
| 6100 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-3,~2\right) $ and $ \vec{v_2} = \left(-4,~2,~4\right) $ . | 1 |
