Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2601 | Determine whether the vectors $ \vec{v_1} = \left(4,~-6\right) $ and $ \vec{v_2} = \left(-7,~6\right) $ are linearly independent or dependent. | 1 |
2602 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~0\right) $ . | 1 |
2603 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-3,~2\right) $ and $ \vec{v_2} = \left(0,~3,~5\right) $ . | 1 |
2604 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~4\right) $ and $ \vec{v_2} = \left(1,~1,~4\right) $ . | 1 |
2605 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~0,~1\right) $ . | 1 |
2606 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(1,~-2,~-4\right) $ . | 1 |
2607 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~3,~-4\right) $ and $ \vec{v_2} = \left(2,~1,~3\right) $ . | 1 |
2608 | Find the angle between vectors $ \left(632,~130\right)$ and $\left(719,~240\right)$. | 1 |
2609 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-1,~1\right) $ and $ \vec{v_2} = \left(4,~5,~-3\right) $ . | 1 |
2610 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ . | 1 |
2611 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~-5\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ . | 1 |
2612 | Find the difference of the vectors $ \vec{v_1} = \left(11,~2,~5\right) $ and $ \vec{v_2} = \left(8,~-4,~20\right) $ . | 1 |
2613 | Find the sum of the vectors $ \vec{v_1} = \left(2,~5,~3\right) $ and $ \vec{v_2} = \left(4,~1,~2\right) $ . | 1 |
2614 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~8\right) $ . | 1 |
2615 | Determine whether the vectors $ \vec{v_1} = \left(10,~-4,~6\right) $, $ \vec{v_2} = \left(-15,~6,~-9\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
2616 | Determine whether the vectors $ \vec{v_1} = \left(4,~-6\right) $ and $ \vec{v_2} = \left(-7,~-3\right) $ are linearly independent or dependent. | 1 |
2617 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~0,~3\right) $ and $ \vec{v_2} = \left(-2,~1,~5\right) $ . | 1 |
2618 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~1,~2\right) $ and $ \vec{v_2} = \left(-1,~0,~2\right) $ . | 1 |
2619 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~3\right) $ and $ \vec{v_2} = \left(5,~-1,~2\right) $ . | 1 |
2620 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5 \sqrt{ 2 },~-3\right) $ and $ \vec{v_2} = \left(17,~-26\right) $ . | 1 |
2621 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-7\right) $ and $ \vec{v_2} = \left(6,~-1\right) $ . | 1 |
2622 | Find the sum of the vectors $ \vec{v_1} = \left(632,~130\right) $ and $ \vec{v_2} = \left(719,~240\right) $ . | 1 |
2623 | Find the difference of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 1 |
2624 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-8\right) $ and $ \vec{v_2} = \left(7,~-7\right) $ . | 1 |
2625 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
2626 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~2\right) $ . | 1 |
2627 | Find the projection of the vector $ \vec{v_1} = \left(2,~5,~3\right) $ on the vector $ \vec{v_2} = \left(4,~1,~2\right) $. | 1 |
2628 | Find the angle between vectors $ \left(-3,~5,~1\right)$ and $\left(-9,~-2,~5\right)$. | 1 |
2629 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~0\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
2630 | Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~-4,~6\right) $ and $ \vec{v_2} = \left(-15,~6,~-9\right) $ . | 1 |
2631 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 1 |
2632 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-5,~-4\right) $ and $ \vec{v_2} = \left(3,~-2,~-1\right) $ . | 1 |
2633 | Find the angle between vectors $ \left(4,~-6\right)$ and $\left(-7,~-3\right)$. | 1 |
2634 | Find the sum of the vectors $ \vec{v_1} = \left(14,~6,~10 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(8,~4,~12 \sqrt{ 3 }\right) $ . | 1 |
2635 | Determine whether the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 5 }{ 2 }\right) $ and $ \vec{v_2} = \left(16,~-30\right) $ are linearly independent or dependent. | 1 |
2636 | 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 |
2637 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~5,~1\right) $ and $ \vec{v_2} = \left(-4,~-1,~-2\right) $ . | 1 |
2638 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~6\right) $ and $ \vec{v_2} = \left(11,~11,~22\right) $ . | 1 |
2639 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5 \sqrt{ 2 },~-3\right) $ . | 1 |
2640 | 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 |
2641 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~60\right) $ . | 1 |
2642 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~9,~-8\right) $ . | 1 |
2643 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-5,~-3\right) $ and $ \vec{v_2} = \left(4,~2,~2\right) $ . | 1 |
2644 | Find the difference of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 1 |
2645 | Find the difference of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ . | 1 |
2646 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(1347,~\dfrac{ 22269 }{ 125 }\right) $ . | 1 |
2647 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-4,~4\right) $ . | 1 |
2648 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-2,~1\right) $ and $ \vec{v_2} = \left(4,~2,~-1\right) $ . | 1 |
2649 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~4\right) $ and $ \vec{v_2} = \left(3,~-9\right) $ . | 1 |
2650 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 9 },~\dfrac{ 5 }{ 9 }\right) $ and $ \vec{v_2} = \left(9,~26\right) $ . | 1 |