Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2701 | Find the difference of the vectors $ \vec{v_1} = \left(0,~\sqrt{ 5 }\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 1 |
2702 | Find the angle between vectors $ \left(-\dfrac{ 1 }{ 2 },~-\dfrac{ 1 }{ 2 },~1\right)$ and $\left(-1,~0,~1\right)$. | 1 |
2703 | Find the sum of the vectors $ \vec{v_1} = \left(16,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 1 |
2704 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-6\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ . | 1 |
2705 | Find the angle between vectors $ \left(3,~5,~1\right)$ and $\left(-9,~2,~5\right)$. | 1 |
2706 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~1,~2\right) $ and $ \vec{v_2} = \left(1,~0,~1\right) $ . | 1 |
2707 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 5645117 }{ 100 },~-\dfrac{ 770859 }{ 50 },~\dfrac{ 429504 }{ 25 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 5643497 }{ 100 },~-\dfrac{ 1541283 }{ 100 },~\dfrac{ 858759 }{ 50 }\right) $ . | 1 |
2708 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-5,~-4\right) $ and $ \vec{v_2} = \left(0,~-4,~-3\right) $ . | 1 |
2709 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~5\right) $ on the vector $ \vec{v_2} = \left(5,~-5,~2\right) $. | 1 |
2710 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(7,~26\right) $ . | 1 |
2711 | Determine whether the vectors $ \vec{v_1} = \left(8,~-12\right) $ and $ \vec{v_2} = \left(40,~-60\right) $ are linearly independent or dependent. | 1 |
2712 | Find the difference 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 |
2713 | 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 |
2714 | 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 |
2715 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 1 |
2716 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3020,~2800\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 1 |
2717 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~0\right) $ . | 1 |
2718 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-5\right) $ . | 1 |
2719 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~309\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
2720 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ . | 1 |
2721 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 5645117 }{ 100 },~-\dfrac{ 770859 }{ 50 },~\dfrac{ 429504 }{ 25 }\right) $ . | 1 |
2722 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 7 }{ 25 },~\dfrac{ 24 }{ 25 }\right) $ . | 1 |
2723 | Find the sum of the vectors $ \vec{v_1} = \left(7,~3,~5 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(6,~3,~9 \sqrt{ 3 }\right) $ . | 1 |
2724 | Find the angle between vectors $ \left(\sqrt{ 3 },~-3\right)$ and $\left(-1,~-1\right)$. | 1 |
2725 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-5\right) $ and $ \vec{v_2} = \left(-1,~0\right) $ . | 1 |
2726 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-6\right) $ . | 1 |
2727 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-2,~4\right) $ . | 1 |
2728 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~2,~0\right) $ and $ \vec{v_2} = \left(2,~2,~-1\right) $ . | 1 |
2729 | 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 |
2730 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-6,~-\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(4,~-3,~1\right) $ . | 1 |
2731 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(1,~-2,~0\right) $ . | 1 |
2732 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 1 |
2733 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~3\right) $ . | 1 |
2734 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~2\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
2735 | Find the angle between vectors $ \left(3,~5,~-1\right)$ and $\left(9,~8,~5\right)$. | 1 |
2736 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~1\right) $ . | 1 |
2737 | Find the sum of the vectors $ \vec{v_1} = \left(10,~-8\right) $ and $ \vec{v_2} = \left(4,~6\right) $ . | 1 |
2738 | Find the sum of the vectors $ \vec{v_1} = \left(75,~-75 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 175 \sqrt{ 3}}{ 4 },~43.75\right) $ . | 1 |
2739 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~5,~1\right) $ and $ \vec{v_2} = \left(-9,~-2,~5\right) $ . | 1 |
2740 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 5645117 }{ 100 },~-\dfrac{ 770859 }{ 50 },~\dfrac{ 429504 }{ 25 }\right) $, $ \vec{v_2} = \left(\dfrac{ 5643497 }{ 100 },~-\dfrac{ 1541283 }{ 100 },~\dfrac{ 858759 }{ 50 }\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
2741 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~0\right) $ and $ \vec{v_2} = \left(2,~-1,~1\right) $ . | 1 |
2742 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-5,~1\right) $ and $ \vec{v_2} = \left(-2,~5,~5\right) $ . | 1 |
2743 | Find the magnitude of the vector $ \| \vec{v} \| = \left(13,~6,~14 \sqrt{ 3 }\right) $ . | 1 |
2744 | Find the angle between vectors $ \left(2,~-3\right)$ and $\left(-3,~-4\right)$. | 1 |
2745 | 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 |
2746 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(1,~-2,~0\right) $ . | 1 |
2747 | Find the difference of the vectors $ \vec{v_1} = \left(9,~0\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
2748 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~2\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
2749 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-3,~4\right) $ and $ \vec{v_2} = \left(1,~5,~0\right) $ . | 1 |
2750 | Find the projection of the vector $ \vec{v_1} = \left(6,~3,~5\right) $ on the vector $ \vec{v_2} = \left(-5,~8,~3\right) $. | 1 |