Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2551 | Find the angle between vectors $ \left(12,~-9,~6\right)$ and $\left(-8,~6,~-4\right)$. | 1 |
2552 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
2553 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4,~6\right) $ . | 1 |
2554 | Determine whether the vectors $ \vec{v_1} = \left(4,~9\right) $ and $ \vec{v_2} = \left(4,~9\right) $ are linearly independent or dependent. | 1 |
2555 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-2\right) $ and $ \vec{v_2} = \left(11,~-6\right) $ . | 1 |
2556 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9,~0,~-3\right) $ and $ \vec{v_2} = \left(0,~7,~0\right) $ . | 1 |
2557 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-4\right) $ . | 1 |
2558 | Find the sum of the vectors $ \vec{v_1} = \left(10,~-5\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ . | 1 |
2559 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~0\right) $ and $ \vec{v_2} = \left(1,~0,~1\right) $ . | 1 |
2560 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
2561 | Find the angle between vectors $ \left(2,~2,~-4\right)$ and $\left(1,~0,~0\right)$. | 1 |
2562 | Find the magnitude of the vector $ \| \vec{v} \| = \left(200,~0\right) $ . | 1 |
2563 | Find the difference of the vectors $ \vec{v_1} = \left(200,~0\right) $ and $ \vec{v_2} = \left(20,~0\right) $ . | 1 |
2564 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~-4\right) $ and $ \vec{v_2} = \left(-3,~1,~-3\right) $ . | 1 |
2565 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-12\right) $ . | 1 |
2566 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~-3,~0\right) $ and $ \vec{v_2} = \left(0,~-2,~-3\right) $ . | 1 |
2567 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ . | 1 |
2568 | Calculate the cross product of the vectors $ \vec{v_1} = \left(11,~-1,~-2\right) $ and $ \vec{v_2} = \left(15,~-1,~-4\right) $ . | 1 |
2569 | Find the magnitude of the vector $ \| \vec{v} \| = \left(13,~4,~-16\right) $ . | 1 |
2570 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6 \sqrt{ 14 },~5\right) $ . | 1 |
2571 | Find the sum of the vectors $ \vec{v_1} = \left(8,~8,~-4\right) $ and $ \vec{v_2} = \left(3,~-6,~9\right) $ . | 1 |
2572 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~0,~-1\right) $ . | 1 |
2573 | Determine whether the vectors $ \vec{v_1} = \left(4,~9\right) $ and $ \vec{v_2} = \left(-4,~-9\right) $ are linearly independent or dependent. | 1 |
2574 | Find the sum of the vectors $ \vec{v_1} = \left(8,~7\right) $ and $ \vec{v_2} = \left(-6,~4\right) $ . | 1 |
2575 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-2\right) $ . | 1 |
2576 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(1,~4,~3\right) $ . | 1 |
2577 | Find the difference of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(-3,~7\right) $ . | 1 |
2578 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(-4,~4\right) $ . | 1 |
2579 | Find the difference of the vectors $ \vec{v_1} = \left(200,~200\right) $ and $ \vec{v_2} = \left(200,~0\right) $ . | 1 |
2580 | Find the angle between vectors $ \left(200,~0\right)$ and $\left(20,~0\right)$. | 1 |
2581 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(0,~0,~7\right) $ . | 1 |
2582 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ . | 1 |
2583 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~8\right) $ . | 1 |
2584 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(2,~-4\right) $ . | 1 |
2585 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\sqrt{ 3 },~5\right) $ and $ \vec{v_2} = \left(4,~-\sqrt{ 3 },~10\right) $ . | 1 |
2586 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~-3\right) $ . | 1 |
2587 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~3,~-5\right) $ and $ \vec{v_2} = \left(-8,~5,~3\right) $ . | 1 |
2588 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~7\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ . | 1 |
2589 | Determine whether the vectors $ \vec{v_1} = \left(1,~1,~1\right) $, $ \vec{v_2} = \left(1,~0,~-1\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
2590 | Find the projection of the vector $ \vec{v_1} = \left(1,~-6\right) $ on the vector $ \vec{v_2} = \left(-15,~8\right) $. | 1 |
2591 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ . | 1 |
2592 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
2593 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
2594 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~3\right) $ . | 1 |
2595 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~0,~3\right) $ and $ \vec{v_2} = \left(-2,~3,~-2\right) $ . | 1 |
2596 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-3,~2\right) $ and $ \vec{v_2} = \left(-7,~-7,~0\right) $ . | 1 |
2597 | Find the projection of the vector $ \vec{v_1} = \left(10,~5\right) $ on the vector $ \vec{v_2} = \left(5,~10\right) $. | 1 |
2598 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
2599 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-8\right) $ and $ \vec{v_2} = \left(7,~-7\right) $ . | 1 |
2600 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~\dfrac{ 3 }{ 2 },~1\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |