Vectors – Solved Problems Database
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,~-5,~1\right) $ . | 1 |
2652 | Find the difference of the vectors $ \vec{v_1} = \left(4851271.3742,~1291753.5681,~517172.499\right) $ and $ \vec{v_2} = \left(14184194,~11081905,~0\right) $ . | 1 |
2653 | 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 |
2654 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-5\right) $ . | 1 |
2655 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2,~-3\right) $ and $ \vec{v_2} = \left(3,~-1,~-1\right) $ . | 1 |
2656 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-7\right) $ . | 1 |
2657 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~5,~2\right) $ and $ \vec{v_2} = \left(3,~-2,~1\right) $ . | 1 |
2658 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(-9,~-3\right) $ . | 1 |
2659 | Find the projection of the vector $ \vec{v_1} = \left(3,~5\right) $ on the vector $ \vec{v_2} = \left(0,~8\right) $. | 1 |
2660 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1500,~1500\right) $ . | 1 |
2661 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~7\right) $ and $ \vec{v_2} = \left(1,~-3\right) $ . | 1 |
2662 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-5,~2\right) $ and $ \vec{v_2} = \left(3,~1,~-10\right) $ . | 1 |
2663 | Find the projection of the vector $ \vec{v_1} = \left(1,~-5,~1\right) $ on the vector $ \vec{v_2} = \left(-2,~5,~5\right) $. | 1 |
2664 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-2\right) $ and $ \vec{v_2} = \left(-6,~4\right) $ . | 1 |
2665 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~3\right) $ . | 1 |
2666 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 5 }{ 2 }\right) $ . | 1 |
2667 | 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 |
2668 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~1,~0\right) $ . | 1 |
2669 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~0,~2\right) $ . | 1 |
2670 | Find the angle between vectors $ \left(4,~2,~-3\right)$ and $\left(3,~-1,~-1\right)$. | 1 |
2671 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
2672 | Find the difference of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 1 |
2673 | Find the projection of the vector $ \vec{v_1} = \left(2,~1,~-1\right) $ on the vector $ \vec{v_2} = \left(1,~5,~2\right) $. | 1 |
2674 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-5,~-3\right) $ and $ \vec{v_2} = \left(4,~2,~2\right) $ . | 1 |
2675 | Find the sum of the vectors $ \vec{v_1} = \left(8,~1\right) $ and $ \vec{v_2} = \left(-7,~-1\right) $ . | 1 |
2676 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~0,~0\right) $ . | 1 |
2677 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-12,~-11\right) $ and $ \vec{v_2} = \left(3,~-2,~-7\right) $ . | 1 |
2678 | Find the difference of the vectors $ \vec{v_1} = \left(-27,~21\right) $ and $ \vec{v_2} = \left(-3,~1\right) $ . | 1 |
2679 | Find the sum of the vectors $ \vec{v_1} = \left(28,~12,~20 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(2,~1,~3 \sqrt{ 3 }\right) $ . | 1 |
2680 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-33,~-12,~-5\right) $ . | 1 |
2681 | Find the angle between vectors $ \left(10,~-3\right)$ and $\left(-5,~-1\right)$. | 1 |
2682 | Calculate the dot product of the vectors $ \vec{v_1} = \left(20,~-15,~0\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
2683 | Find the sum of the vectors $ \vec{v_1} = \left(3,~8\right) $ and $ \vec{v_2} = \left(2,~9\right) $ . | 1 |
2684 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-2,~3\right) $ and $ \vec{v_2} = \left(3,~-1,~2\right) $ . | 1 |
2685 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3020,~280\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 1 |
2686 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
2687 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 1 |
2688 | Find the angle between vectors $ \left(3,~-4,~4\right)$ and $\left(2,~3,~-7\right)$. | 1 |
2689 | Determine whether the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ are linearly independent or dependent. | 1 |
2690 | Find the sum of the vectors $ \vec{v_1} = \left(1,~11\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ . | 1 |
2691 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~-4\right) $ . | 1 |
2692 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~0\right) $ and $ \vec{v_2} = \left(9,~26\right) $ . | 1 |
2693 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-2,~-7\right) $ and $ \vec{v_2} = \left(-15,~-9,~-11\right) $ . | 1 |
2694 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~5\right) $ and $ \vec{v_2} = \left(6,~2,~5\right) $ . | 1 |
2695 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~9\right) $ and $ \vec{v_2} = \left(14,~-12\right) $ . | 1 |
2696 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0,~0\right) $ and $ \vec{v_2} = \left(-5,~5,~1\right) $ . | 1 |
2697 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~0,~2\right) $ . | 1 |
2698 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~-6\right) $ and $ \vec{v_2} = \left(-5,~15,~-25\right) $ . | 1 |
2699 | Find the difference of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 1 |
2700 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~-1,~3\right) $ . | 1 |