Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5001 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-5,~-2\right) $ and $ \vec{v_2} = \left(8,~7,~0\right) $ . | 1 |
| 5002 | Find the magnitude of the vector $ \| \vec{v} \| = \left(14,~2,~-2\right) $ . | 1 |
| 5003 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4,~6\right) $ . | 1 |
| 5004 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-2\right) $ . | 1 |
| 5005 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-2\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 1 |
| 5006 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~7\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ . | 1 |
| 5007 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~8\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ . | 1 |
| 5008 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~5,~3\right) $ and $ \vec{v_2} = \left(3,~-1,~-6\right) $ . | 1 |
| 5009 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~-6\right) $ and $ \vec{v_2} = \left(6,~5,~3\right) $ . | 1 |
| 5010 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-5,~-3\right) $ and $ \vec{v_2} = \left(3,~-1,~-6\right) $ . | 1 |
| 5011 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1,~-7\right) $ and $ \vec{v_2} = \left(-1,~-7,~-3\right) $ . | 1 |
| 5012 | Find the difference of the vectors $ \vec{v_1} = \left(-10,~3\right) $ and $ \vec{v_2} = \left(-7,~-9\right) $ . | 1 |
| 5013 | Determine whether the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(-24,~40\right) $ are linearly independent or dependent. | 1 |
| 5014 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~2\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 1 |
| 5015 | Find the angle between vectors $ \left(-5,~2\right)$ and $\left(-3,~7\right)$. | 1 |
| 5016 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(16,~40\right) $ . | 1 |
| 5017 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $ and $ \vec{v_2} = \left(-1,~-1,~5\right) $ . | 1 |
| 5018 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~0\right) $ and $ \vec{v_2} = \left(1,~7,~2\right) $ . | 1 |
| 5019 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-6\right) $ . | 1 |
| 5020 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~4\right) $ and $ \vec{v_2} = \left(3,~-9\right) $ . | 1 |
| 5021 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~7\right) $ and $ \vec{v_2} = \left(9,~1\right) $ . | 1 |
| 5022 | Find the angle between vectors $ \left(6,~7\right)$ and $\left(9,~1\right)$. | 1 |
| 5023 | Find the sum of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(9,~7\right) $ . | 1 |
| 5024 | Find the difference of the vectors $ \vec{v_1} = \left(-12,~21\right) $ and $ \vec{v_2} = \left(8,~-20\right) $ . | 1 |
| 5025 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2.9,~3.07\right) $ . | 1 |
| 5026 | Calculate the dot product of the vectors $ \vec{v_1} = \left(240,~300\right) $ and $ \vec{v_2} = \left(2.9,~3.08\right) $ . | 1 |
| 5027 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 9 },~\dfrac{ 5 }{ 9 }\right) $ and $ \vec{v_2} = \left(9,~26\right) $ . | 1 |
| 5028 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~0\right) $ and $ \vec{v_2} = \left(9,~26\right) $ . | 1 |
| 5029 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(7,~26\right) $ . | 1 |
| 5030 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 9 }{ 41 },~\dfrac{ 40 }{ 41 }\right) $ . | 1 |
| 5031 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 6 }{ 5 },~-\dfrac{ 12 }{ 5 }\right) $ . | 1 |
| 5032 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 6 }{ 5 },~-\dfrac{ 12 }{ 5 }\right) $ and $ \vec{v_2} = \left(28,~96\right) $ . | 1 |
| 5033 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 36 }{ 41 },~-\dfrac{ 160 }{ 41 }\right) $ . | 1 |
| 5034 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 8 }{ 17 },~\dfrac{ 15 }{ 17 }\right) $ . | 1 |
| 5035 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~10\right) $ . | 1 |
| 5036 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 15 }{ 13 },~-\dfrac{ 36 }{ 13 }\right) $ . | 1 |
| 5037 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 4 }{ 9 },~\dfrac{ 5 }{ 9 }\right) $ . | 1 |
| 5038 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~40\right) $ . | 1 |
| 5039 | Find the sum of the vectors $ \vec{v_1} = \left(9,~9\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 1 |
| 5040 | Find the difference of the vectors $ \vec{v_1} = \left(9,~9\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 1 |
| 5041 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~0\right) $ . | 1 |
| 5042 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~0\right) $ and $ \vec{v_2} = \left(-3.5355,~-3.5355\right) $ . | 1 |
| 5043 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~0\right) $ and $ \vec{v_2} = \left(-3.5355,~-3.5355\right) $ . | 1 |
| 5044 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-4,~-3\right) $ and $ \vec{v_2} = \left(2,~4,~5\right) $ . | 1 |
| 5045 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-4,~-3\right) $ and $ \vec{v_2} = \left(5,~-5,~3\right) $ . | 1 |
| 5046 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4,~5\right) $ and $ \vec{v_2} = \left(5,~-5,~3\right) $ . | 1 |
| 5047 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4,~5\right) $ and $ \vec{v_2} = \left(2,~4,~5\right) $ . | 1 |
| 5048 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-4,~-3\right) $ and $ \vec{v_2} = \left(7,~-1,~8\right) $ . | 1 |
| 5049 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 7 },~\dfrac{ 6 }{ 7 }\right) $ and $ \vec{v_2} = \left(4,~29\right) $ . | 1 |
| 5050 | Find the projection of the vector $ \vec{v_1} = \left(-3,~5\right) $ on the vector $ \vec{v_2} = \left(-1,~5\right) $. | 1 |
