Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2651 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-1,~-4\right) $ . | 1 |
| 2652 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~-1,~2\right) $ . | 1 |
| 2653 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(-6,~6\right) $ . | 1 |
| 2654 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(-1,~2,~1\right) $ . | 1 |
| 2655 | Find the projection of the vector $ \vec{v_1} = \left(1,~-2,~3\right) $ on the vector $ \vec{v_2} = \left(-1,~2,~1\right) $. | 1 |
| 2656 | Find the angle between vectors $ \left(6,~-2,~2\right)$ and $\left(0,~2,~-6\right)$. | 1 |
| 2657 | Find the angle between vectors $ \left(-12,~4,~0\right)$ and $\left(0,~2,~-6\right)$. | 1 |
| 2658 | Find the angle between vectors $ \left(-12,~4,~0\right)$ and $\left(6,~-2,~2\right)$. | 1 |
| 2659 | Determine whether the vectors $ \vec{v_1} = \left(2,~7,~3\right) $, $ \vec{v_2} = \left(1,~5,~8\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 2660 | Determine whether the vectors $ \vec{v_1} = \left(6,~-23\right) $ and $ \vec{v_2} = \left(46,~-12\right) $ are linearly independent or dependent. | 1 |
| 2661 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~0\right) $ and $ \vec{v_2} = \left(3,~-1,~2\right) $ . | 1 |
| 2662 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(-4,~4\right) $ . | 1 |
| 2663 | Calculate the dot product of the vectors $ \vec{v_1} = \left(255,~255\right) $ and $ \vec{v_2} = \left(-150,~-300\right) $ . | 1 |
| 2664 | Find the angle between vectors $ \left(255,~255\right)$ and $\left(-150,~-300\right)$. | 1 |
| 2665 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~9,~-3\right) $ and $ \vec{v_2} = \left(1,~2,~-4\right) $ . | 1 |
| 2666 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-6,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-1\right) $ . | 1 |
| 2667 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-6,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-1\right) $ . | 1 |
| 2668 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-7,~0\right) $ and $ \vec{v_2} = \left(5,~-5,~2\right) $ . | 1 |
| 2669 | Find the projection of the vector $ \vec{v_1} = \left(4,~3\right) $ on the vector $ \vec{v_2} = \left(2,~3\right) $. | 1 |
| 2670 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 1 |
| 2671 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~0,~2\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
| 2672 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~0,~2\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
| 2673 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~0,~2\right) $ and $ \vec{v_2} = \left(0,~1,~-1\right) $ . | 1 |
| 2674 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1,~-1\right) $ and $ \vec{v_2} = \left(0,~1,~-1\right) $ . | 1 |
| 2675 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~1\right) $ and $ \vec{v_2} = \left(0,~1,~-1\right) $ . | 1 |
| 2676 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~1,~13\right) $ and $ \vec{v_2} = \left(-1,~3,~3\right) $ . | 1 |
| 2677 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~1,~13\right) $ and $ \vec{v_2} = \left(-1,~3,~3\right) $ . | 1 |
| 2678 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 1 |
| 2679 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-12,~15\right) $ and $ \vec{v_2} = \left(2,~2,~14\right) $ . | 1 |
| 2680 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~8\right) $ . | 1 |
| 2681 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~-8,~0\right) $ . | 1 |
| 2682 | Find the angle between vectors $ \left(7,~-8,~0\right)$ and $\left(1,~1,~0\right)$. | 1 |
| 2683 | Find the difference of the vectors $ \vec{v_1} = \left(7,~-8,~0\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
| 2684 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~-7\right) $ and $ \vec{v_2} = \left(2,~-1,~7\right) $ . | 1 |
| 2685 | Find the difference of the vectors $ \vec{v_1} = \left(-9,~28\right) $ and $ \vec{v_2} = \left(5,~7\right) $ . | 1 |
| 2686 | Find the difference of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
| 2687 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~-1,~0\right) $ . | 1 |
| 2688 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
| 2689 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~-1\right) $ and $ \vec{v_2} = \left(-1,~0,~0\right) $ . | 1 |
| 2690 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~0,~-1\right) $ . | 1 |
| 2691 | Find the angle between vectors $ \left(-2,~1,~1\right)$ and $\left(1,~-3,~-1\right)$. | 1 |
| 2692 | Find the angle between vectors $ \left(6,~-4,~1\right)$ and $\left(3,~-2,~-3\right)$. | 1 |
| 2693 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-4,~1\right) $ and $ \vec{v_2} = \left(3,~-2,~-3\right) $ . | 1 |
| 2694 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~1\right) $ . | 1 |
| 2695 | Find the difference of the vectors $ \vec{v_1} = \left(70,~90\right) $ and $ \vec{v_2} = \left(120,~210\right) $ . | 1 |
| 2696 | Find the difference of the vectors $ \vec{v_1} = \left(70,~90\right) $ and $ \vec{v_2} = \left(-120,~-210\right) $ . | 1 |
| 2697 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~-1\right) $ and $ \vec{v_2} = \left(-2,~2,~3\right) $ . | 1 |
| 2698 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-4,~0\right) $ and $ \vec{v_2} = \left(4,~2,~0\right) $ . | 1 |
| 2699 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~1,~4\right) $ and $ \vec{v_2} = \left(0,~-7,~4\right) $ . | 1 |
| 2700 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~8\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ . | 1 |
