Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4751 | Find the difference of the vectors $ \vec{v_1} = \left(12,~4,~20 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(3,~0,~9 \sqrt{ 3 }\right) $ . | 1 |
| 4752 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1,~5 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(9,~0,~27 \sqrt{ 3 }\right) $ . | 1 |
| 4753 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~1,~32 \sqrt{ 3 }\right) $ . | 1 |
| 4754 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~-1\right) $ and $ \vec{v_2} = \left(25,~0,~0\right) $ . | 1 |
| 4755 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~-2\right) $ and $ \vec{v_2} = \left(1,~2,~-2\right) $ . | 1 |
| 4756 | Find the difference of the vectors $ \vec{v_1} = \left(4,~0,~-2\right) $ and $ \vec{v_2} = \left(-2,~-3,~2\right) $ . | 1 |
| 4757 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~0,~-5\right) $ and $ \vec{v_2} = \left(-2,~-3,~2\right) $ . | 1 |
| 4758 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-7\right) $ . | 1 |
| 4759 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~0,~3\right) $ and $ \vec{v_2} = \left(-7,~1,~3\right) $ . | 1 |
| 4760 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(7,~5\right) $ . | 1 |
| 4761 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~4\right) $ and $ \vec{v_2} = \left(-9,~8\right) $ . | 1 |
| 4762 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(0,~0,~7\right) $ . | 1 |
| 4763 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-3,~2\right) $ and $ \vec{v_2} = \left(-7,~-7,~0\right) $ . | 1 |
| 4764 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-3,~2\right) $ and $ \vec{v_2} = \left(0,~3,~5\right) $ . | 1 |
| 4765 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~1,~2\right) $ and $ \vec{v_2} = \left(-1,~0,~2\right) $ . | 1 |
| 4766 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~2,~0\right) $ and $ \vec{v_2} = \left(2,~2,~-1\right) $ . | 1 |
| 4767 | Find the angle between vectors $ \left(3,~2,~5\right)$ and $\left(4,~1,~3\right)$. | 1 |
| 4768 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~-3\right) $ and $ \vec{v_2} = \left(-\dfrac{ 253 }{ 50 },~\dfrac{ 199 }{ 25 },~\dfrac{ 407 }{ 50 }\right) $ . | 1 |
| 4769 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~-3\right) $ and $ \vec{v_2} = \left(\dfrac{ 847 }{ 100 },~-\dfrac{ 359 }{ 100 },~\dfrac{ 123 }{ 25 }\right) $ . | 1 |
| 4770 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~5\right) $ . | 1 |
| 4771 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~-2\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
| 4772 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~-2\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
| 4773 | Find the difference of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(6,~0\right) $ . | 1 |
| 4774 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-14\right) $ . | 1 |
| 4775 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-3,~-4\right) $ . | 1 |
| 4776 | Find the sum of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
| 4777 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
| 4778 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 154 }{ 5 },~-22\right) $ . | 1 |
| 4779 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~\dfrac{ 154 }{ 5 },~-22\right) $ . | 1 |
| 4780 | Find the projection of the vector $ \vec{v_1} = \left(0,~\dfrac{ 154 }{ 5 },~-22\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $. | 1 |
| 4781 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~3,~-8\right) $ . | 1 |
| 4782 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0,~0\right) $ and $ \vec{v_2} = \left(-5,~5,~1\right) $ . | 1 |
| 4783 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0.06,~0.075,~0\right) $ and $ \vec{v_2} = \left(0,~-216.5,~125\right) $ . | 1 |
| 4784 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-2,~0\right) $ and $ \vec{v_2} = \left(-1,~-2,~2\right) $ . | 1 |
| 4785 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~0,~2\right) $ . | 1 |
| 4786 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~0,~2\right) $ . | 1 |
| 4787 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~0,~2\right) $ . | 1 |
| 4788 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~0,~2\right) $ . | 1 |
| 4789 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~0,~2\right) $ . | 1 |
| 4790 | | 1 |
| 4791 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~84\right) $ . | 1 |
| 4792 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~84\right) $ and $ \vec{v_2} = \left(1,~53\right) $ . | 1 |
| 4793 | Calculate the dot product of the vectors $ \vec{v_1} = \left(84,~84\right) $ and $ \vec{v_2} = \left(53,~53\right) $ . | 1 |
| 4794 | Find the difference of the vectors $ \vec{v_1} = \left(84,~84\right) $ and $ \vec{v_2} = \left(53,~53\right) $ . | 1 |
| 4795 | 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 |
| 4796 | Find the angle between vectors $ \left(10,~0\right)$ and $\left(15,~0\right)$. | 1 |
| 4797 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(\dfrac{ 9 }{ 20 },~\dfrac{ 9 }{ 20 },~-\dfrac{ 4 }{ 5 }\right) $ . | 1 |
| 4798 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(\dfrac{ 9 }{ 20 },~\dfrac{ 9 }{ 20 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
| 4799 | Find the sum of the vectors $ \vec{v_1} = \left(6,~6,~-7\right) $ and $ \vec{v_2} = \left(-6,~2,~12\right) $ . | 1 |
| 4800 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-3,~-1\right) $ . | 1 |
