Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2601 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~-4\right) $ and $ \vec{v_2} = \left(2,~-8\right) $ . | 1 |
| 2602 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-2\right) $ and $ \vec{v_2} = \left(8,~-6\right) $ . | 1 |
| 2603 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 1 |
| 2604 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ . | 1 |
| 2605 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $. | 1 |
| 2606 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 1 |
| 2607 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-4\right) $ . | 1 |
| 2608 | Find the angle between vectors $ \left(3,~-4\right)$ and $\left(5,~2\right)$. | 1 |
| 2609 | Find the angle between vectors $ \left(3,~7\right)$ and $\left(1,~8\right)$. | 1 |
| 2610 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4 \sqrt{ 3 },~4\right) $ . | 1 |
| 2611 | Find the projection of the vector $ \vec{v_1} = \left(2,~2\right) $ on the vector $ \vec{v_2} = \left(2,~8\right) $. | 1 |
| 2612 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~7\right) $ . | 1 |
| 2613 | Find the projection of the vector $ \vec{v_1} = \left(3,~-8\right) $ on the vector $ \vec{v_2} = \left(3,~-8\right) $. | 1 |
| 2614 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1,~-1\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
| 2615 | Find the angle between vectors $ \left(3,~1,~-1\right)$ and $\left(0,~-2,~2\right)$. | 1 |
| 2616 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~-1\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
| 2617 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~-1\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
| 2618 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
| 2619 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 5 }{ 2 },~-6\right) $ and $ \vec{v_2} = \left(2,~-3,~-6\right) $ . | 1 |
| 2620 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-33,~-12,~-5\right) $ . | 1 |
| 2621 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-12\right) $ . | 1 |
| 2622 | Find the angle between vectors $ \left(0,~-12\right)$ and $\left(10,~6\right)$. | 1 |
| 2623 | Find the angle between vectors $ \left(2,~-1,~4\right)$ and $\left(0,~1,~1\right)$. | 1 |
| 2624 | Find the difference of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 1 |
| 2625 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-2\right) $ . | 1 |
| 2626 | Find the angle between vectors $ \left(-10,~0,~6\right)$ and $\left(1,~3,~5\right)$. | 1 |
| 2627 | Find the angle between vectors $ \left(-11,~0,~6\right)$ and $\left(1,~2,~3\right)$. | 1 |
| 2628 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~-1\right) $ and $ \vec{v_2} = \left(1,~-1,~-1\right) $ . | 1 |
| 2629 | Find the difference of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(-3,~7\right) $ . | 1 |
| 2630 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~1\right) $ and $ \vec{v_2} = \left(3,~1,~1\right) $ . | 1 |
| 2631 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(3,~1,~1\right) $ . | 1 |
| 2632 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0\right) $ . | 1 |
| 2633 | Determine whether the vectors $ \vec{v_1} = \left(5,~2,~-7\right) $, $ \vec{v_2} = \left(-2,~3,~-5\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 2634 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 1 |
| 2635 | Calculate the dot product of the vectors $ \vec{v_1} = \left(21,~12\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ . | 1 |
| 2636 | Find the magnitude of the vector $ \| \vec{v} \| = \left(126,~316\right) $ . | 1 |
| 2637 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 3 },~-\dfrac{ 8 }{ 9 },~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 8 }{ 3 },~1,~0\right) $ . | 1 |
| 2638 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(1,~6\right) $ . | 1 |
| 2639 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ are linearly independent or dependent. | 1 |
| 2640 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~-2\right) $ and $ \vec{v_2} = \left(0,~4,~2\right) $ . | 1 |
| 2641 | Calculate the dot product of the vectors $ \vec{v_1} = \left(14,~-4,~8\right) $ and $ \vec{v_2} = \left(-2,~1,~4\right) $ . | 1 |
| 2642 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-4,~0\right) $ and $ \vec{v_2} = \left(6,~-5,~2\right) $ . | 1 |
| 2643 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-4,~0\right) $ and $ \vec{v_2} = \left(6,~-5,~2\right) $ . | 1 |
| 2644 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~1,~0\right) $ and $ \vec{v_2} = \left(0,~-1,~1\right) $ . | 1 |
| 2645 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~6\right) $ . | 1 |
| 2646 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~0\right) $ . | 1 |
| 2647 | Find the difference of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(7,~-8\right) $ . | 1 |
| 2648 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-1,~3,~-2\right) $ . | 1 |
| 2649 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-1,~3,~-2\right) $ . | 1 |
| 2650 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-2,~-2\right) $ . | 1 |
