Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3701 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-8,~0\right) $ and $ \vec{v_2} = \left(-4,~4,~-1\right) $ . | 1 |
| 3702 | Find the angle between vectors $ \left(4,~-1\right)$ and $\left(-4,~0\right)$. | 1 |
| 3703 | Find the angle between vectors $ \left(0,~-1,~-9\right)$ and $\left(7,~9,~-7\right)$. | 1 |
| 3704 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(-1,~4,~2\right) $ . | 1 |
| 3705 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~4,~2\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 1 |
| 3706 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~6,~3\right) $ and $ \vec{v_2} = \left(3,~3,~-2\right) $ . | 1 |
| 3707 | Find the projection of the vector $ \vec{v_1} = \left(-4,~8\right) $ on the vector $ \vec{v_2} = \left(-5,~-2\right) $. | 1 |
| 3708 | Find the projection of the vector $ \vec{v_1} = \left(-3,~-5,~-1\right) $ on the vector $ \vec{v_2} = \left(-9,~4,~1\right) $. | 1 |
| 3709 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-9,~2,~7\right) $ and $ \vec{v_2} = \left(3,~-7,~0\right) $ . | 1 |
| 3710 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~2,~6\right) $ and $ \vec{v_2} = \left(0,~-8,~3\right) $ . | 1 |
| 3711 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~-1\right) $ and $ \vec{v_2} = \left(4,~6,~-2\right) $ . | 1 |
| 3712 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~-3\right) $ . | 1 |
| 3713 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2,~8\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3714 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2,~8\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3715 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~0\right) $ . | 1 |
| 3716 | Find the angle between vectors $ \left(2,~1,~0\right)$ and $\left(3,~-1,~1\right)$. | 1 |
| 3717 | Find the angle between vectors $ \left(\sqrt{ 3 },~4,~-1\right)$ and $\left(1,~-4,~\sqrt{ 3 }\right)$. | 1 |
| 3718 | Find the angle between vectors $ \left(3,~6,~-2\right)$ and $\left(2,~-2,~1\right)$. | 1 |
| 3719 | Find the angle between vectors $ \left(1,~0,~1\right)$ and $\left(1,~1,~0\right)$. | 1 |
| 3720 | Find the angle between vectors $ \left(1,~1,~0\right)$ and $\left(1,~2,~2\right)$. | 1 |
| 3721 | Find the angle between vectors $ \left(2,~2,~-1\right)$ and $\left(-4,~0,~-3\right)$. | 1 |
| 3722 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(3,~-4,~2\right) $ . | 1 |
| 3723 | Find the angle between vectors $ \left(3,~2,~0\right)$ and $\left(1,~1,~-\sqrt{ 11 }\right)$. | 1 |
| 3724 | Find the angle between vectors $ \left(1,~2,~2\right)$ and $\left(2,~-4,~4\right)$. | 1 |
| 3725 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
| 3726 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~0\right) $ . | 1 |
| 3727 | Find the difference of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 1 |
| 3728 | Find the projection of the vector $ \vec{v_1} = \left(5,~90\right) $ on the vector $ \vec{v_2} = \left(10,~0\right) $. | 1 |
| 3729 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-4\right) $ and $ \vec{v_2} = \left(1,~-4\right) $ . | 1 |
| 3730 | Find the angle between vectors $ \left(2,~-1,~1\right)$ and $\left(1,~1,~2\right)$. | 1 |
| 3731 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~2\right) $ on the vector $ \vec{v_2} = \left(2,~-1,~1\right) $. | 1 |
| 3732 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1,~2\right) $ and $ \vec{v_2} = \left(1,~-\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right) $ . | 1 |
| 3733 | Determine whether the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent. | 1 |
| 3734 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 1 |
| 3735 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 1 |
| 3736 | Find the angle between vectors $ \left(16,~4,~-2\right)$ and $\left(8,~2,~-1\right)$. | 1 |
| 3737 | Find the sum of the vectors $ \vec{v_1} = \left(5,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-3,~2\right) $ . | 1 |
| 3738 | Find the difference of the vectors $ \vec{v_1} = \left(5,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-3,~2\right) $ . | 1 |
| 3739 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-1,~1\right) $ and $ \vec{v_2} = \left(4,~5,~-3\right) $ . | 1 |
| 3740 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(4,~3,~-5\right) $ . | 1 |
| 3741 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-2 \sqrt{ 3 }\right) $ . | 1 |
| 3742 | Find the angle between vectors $ \left(2,~-2 \sqrt{ 3 }\right)$ and $\left(1,~0\right)$. | 1 |
| 3743 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 67 }{ 10 },~\dfrac{ 5 }{ 2 },~0\right) $ . | 1 |
| 3744 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 8 }{ 5 },~\dfrac{ 5 }{ 2 },~0\right) $ . | 1 |
| 3745 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 83 }{ 10 },~0,~0\right) $ . | 1 |
| 3746 | Find the magnitude of the vector $ \| \vec{v} \| = \left(15,~-\dfrac{ 5 }{ 2 },~0\right) $ . | 1 |
| 3747 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~0,~1\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 1 |
| 3748 | Find the angle between vectors $ \left(\dfrac{ 11 }{ 5 },~\dfrac{ 94 }{ 25 }\right)$ and $\left(1,~\dfrac{ 11 }{ 5 }\right)$. | 1 |
| 3749 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~8,~10\right) $ and $ \vec{v_2} = \left(5,~1,~-3\right) $ . | 1 |
| 3750 | Find the angle between vectors $ \left(-4,~8,~10\right)$ and $\left(5,~1,~-3\right)$. | 1 |
