Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5651 | Find the difference of the vectors $ \vec{v_1} = \left(1,~5\right) $ and $ \vec{v_2} = \left(-2,~-3\right) $ . | 1 |
5652 | Find the sum of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ . | 1 |
5653 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
5654 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~-3\right) $ . | 1 |
5655 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~8,~1\right) $ and $ \vec{v_2} = \left(-5,~1,~8\right) $ . | 1 |
5656 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ . | 1 |
5657 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-4,~0\right) $ and $ \vec{v_2} = \left(-4,~7,~0\right) $ . | 1 |
5658 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-4,~0\right) $ and $ \vec{v_2} = \left(-3,~8,~0\right) $ . | 1 |
5659 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-3\right) $ . | 1 |
5660 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~4\right) $ and $ \vec{v_2} = \left(2,~0,~-3\right) $ . | 1 |
5661 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~-2\right) $ and $ \vec{v_2} = \left(0,~-1,~-2\right) $ . | 1 |
5662 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~6\right) $ . | 1 |
5663 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-6,~-1\right) $ and $ \vec{v_2} = \left(7,~-11,~9\right) $ . | 1 |
5664 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~3,~-2\right) $ and $ \vec{v_2} = \left(-3,~5,~3\right) $ . | 1 |
5665 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~4\right) $ . | 1 |
5666 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-32,~56,~32\right) $ . | 1 |
5667 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 6879 }{ 5000 },~-0.192,~-1\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
5668 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~4,~1\right) $ and $ \vec{v_2} = \left(2,~0,~0\right) $ . | 1 |
5669 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~-1\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 1 |
5670 | Find the difference of the vectors $ \vec{v_1} = \left(-9,~9\right) $ and $ \vec{v_2} = \left(4,~6\right) $ . | 1 |
5671 | Find the difference of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(1,~2,~0\right) $ . | 1 |
5672 | Find the angle between vectors $ \left(4,~-2,~5\right)$ and $\left(5,~-4,~-2\right)$. | 1 |
5673 | Find the projection of the vector $ \vec{v_1} = \left(-4,~0,~1\right) $ on the vector $ \vec{v_2} = \left(1,~4,~-4\right) $. | 1 |
5674 | Find the projection of the vector $ \vec{v_1} = \left(-6,~-\dfrac{ 9 }{ 2 },~0\right) $ on the vector $ \vec{v_2} = \left(-6,~2,~3\right) $. | 1 |
5675 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~-5\right) $ and $ \vec{v_2} = \left(-6,~-4\right) $ . | 1 |
5676 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-3\right) $ . | 1 |
5677 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
5678 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~1\right) $ . | 1 |
5679 | Find the projection of the vector $ \vec{v_1} = \left(2,~0\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 1 |
5680 | Find the projection of the vector $ \vec{v_1} = \left(-7,~3,~2\right) $ on the vector $ \vec{v_2} = \left(5,~0,~-1\right) $. | 1 |
5681 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-6\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
5682 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~35\right) $ and $ \vec{v_2} = \left(60,~-11\right) $ . | 1 |
5683 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1\right) $ . | 1 |
5684 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 113701 }{ 10000 },~\dfrac{ 630253 }{ 100000 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 51 }{ 5 },~-\dfrac{ 68 }{ 5 },~0\right) $ . | 1 |
5685 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~-1,~0\right) $ and $ \vec{v_2} = \left(-1,~-2,~0\right) $ . | 1 |
5686 | Find the projection of the vector $ \vec{v_1} = \left(4,~-2,~5\right) $ on the vector $ \vec{v_2} = \left(5,~-4,~-2\right) $. | 1 |
5687 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 1 |
5688 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~3\right) $ and $ \vec{v_2} = \left(6,~6,~6\right) $ . | 1 |
5689 | Find the projection of the vector $ \vec{v_1} = \left(-1,~-10,~8\right) $ on the vector $ \vec{v_2} = \left(3,~1,~-1\right) $. | 1 |
5690 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-14,~5\right) $ . | 1 |
5691 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(16,~40\right) $ . | 1 |
5692 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-6,~-1\right) $ and $ \vec{v_2} = \left(11,~5,~-9\right) $ . | 1 |
5693 | Find the angle between vectors $ \left(2,~3\right)$ and $\left(0,~1\right)$. | 1 |
5694 | Find the angle between vectors $ \left(-\dfrac{ 6879 }{ 5000 },~-0.192,~-1\right)$ and $\left(0,~1,~0\right)$. | 1 |
5695 | Find the projection of the vector $ \vec{v_1} = \left(-1,~3\right) $ on the vector $ \vec{v_2} = \left(-1,~-2\right) $. | 1 |
5696 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
5697 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(3,~-7\right) $ . | 1 |
5698 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~2 \sqrt{ 3 }\right) $ . | 1 |
5699 | Find the projection of the vector $ \vec{v_1} = \left(-2,~7,~-3\right) $ on the vector $ \vec{v_2} = \left(-1,~3,~1\right) $. | 1 |
5700 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-1,~1\right) $ . | 1 |