Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5551 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-45\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 1 |
5552 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~40\right) $ . | 1 |
5553 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 4139 }{ 200 },~\dfrac{ 2143 }{ 250 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 399 }{ 40 },~\dfrac{ 3748 }{ 125 }\right) $ . | 1 |
5554 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-4,~3\right) $ and $ \vec{v_2} = \left(3,~-1,~-2\right) $ . | 1 |
5555 | Find the projection of the vector $ \vec{v_1} = \left(1,~-2\right) $ on the vector $ \vec{v_2} = \left(-4,~10\right) $. | 1 |
5556 | Find the angle between vectors $ \left(5,~-5\right)$ and $\left(-10,~10\right)$. | 1 |
5557 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
5558 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 113701 }{ 10000 },~\dfrac{ 630253 }{ 100000 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 51 }{ 5 },~-\dfrac{ 68 }{ 5 }\right) $ . | 1 |
5559 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~1,~-2\right) $ and $ \vec{v_2} = \left(10,~3,~-6\right) $ . | 1 |
5560 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~-6\right) $ . | 1 |
5561 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4,~-5\right) $ and $ \vec{v_2} = \left(-15,~15,~-18\right) $ . | 1 |
5562 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
5563 | Determine whether the vectors $ \vec{v_1} = \left(15,~30\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ are linearly independent or dependent. | 1 |
5564 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~4,~4\right) $ . | 1 |
5565 | Find the angle between vectors $ \left(7,~-1\right)$ and $\left(1,~4\right)$. | 1 |
5566 | Find the angle between vectors $ \left(5,~3,~5\right)$ and $\left(3,~2,~2\right)$. | 1 |
5567 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~8\right) $ and $ \vec{v_2} = \left(-9,~3\right) $ . | 1 |
5568 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 1 |
5569 | Find the difference of the vectors $ \vec{v_1} = \left(-9,~28\right) $ and $ \vec{v_2} = \left(5,~7\right) $ . | 1 |
5570 | Find the angle between vectors $ \left(-4,~-5\right)$ and $\left(1,~3\right)$. | 1 |
5571 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0,~1\right) $ and $ \vec{v_2} = \left(-2,~-11,~2\right) $ . | 1 |
5572 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 1 |
5573 | Find the sum of the vectors $ \vec{v_1} = \left(4,~8\right) $ and $ \vec{v_2} = \left(10,~10\right) $ . | 1 |
5574 | Find the projection of the vector $ \vec{v_1} = \left(-4,~10\right) $ on the vector $ \vec{v_2} = \left(1,~-2\right) $. | 1 |
5575 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-1\right) $ and $ \vec{v_2} = \left(1,~-6\right) $ . | 1 |
5576 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2,~8\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
5577 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~-2\right) $ and $ \vec{v_2} = \left(3,~-2,~-4\right) $ . | 1 |
5578 | Find the angle between vectors $ \left(4,~-2,~5\right)$ and $\left(1,~3,~2\right)$. | 1 |
5579 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~3,~-8\right) $ and $ \vec{v_2} = \left(2,~-2,~-3\right) $ . | 1 |
5580 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-7\right) $ and $ \vec{v_2} = \left(1,~-2\right) $ . | 1 |
5581 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~5\right) $ . | 1 |
5582 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-4\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ . | 1 |
5583 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-21,~15,~-38\right) $ . | 1 |
5584 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-4\right) $ and $ \vec{v_2} = \left(-9,~-5\right) $ . | 1 |
5585 | Find the sum of the vectors $ \vec{v_1} = \left(3,~9\right) $ and $ \vec{v_2} = \left(-6,~-7\right) $ . | 1 |
5586 | Find the angle between vectors $ \left(5,~3,~5\right)$ and $\left(-10,~0,~10\right)$. | 1 |
5587 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-1\right) $ . | 1 |
5588 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~8,~1\right) $ and $ \vec{v_2} = \left(-5,~1,~8\right) $ . | 1 |
5589 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-1,~2\right) $ . | 1 |
5590 | Find the angle between vectors $ \left(3,~-4\right)$ and $\left(-4,~7\right)$. | 1 |
5591 | Find the sum of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
5592 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~-5\right) $ . | 1 |
5593 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~2,~-4\right) $ and $ \vec{v_2} = \left(-2,~9,~-2\right) $ . | 1 |
5594 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-6,~-1\right) $ and $ \vec{v_2} = \left(33,~21,~-27\right) $ . | 1 |
5595 | | 1 |
5596 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~-3\right) $ . | 1 |
5597 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1,~0\right) $, $ \vec{v_2} = \left(2,~0,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
5598 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0\right) $ . | 1 |
5599 | Find the angle between vectors $ \left(3,~6\right)$ and $\left(\sqrt{ 2 },~-\dfrac{ 1 }{ 3 }\right)$. | 1 |
5600 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~3\right) $ and $ \vec{v_2} = \left(2,~3,~4\right) $ . | 1 |