Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1001 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~1\right) $ . | 2 |
1002 | Find the angle between vectors $ \left(6,~8\right)$ and $\left(2,~0\right)$. | 2 |
1003 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~2\right) $ and $ \vec{v_2} = \left(-1,~5,~-2\right) $ . | 2 |
1004 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ . | 2 |
1005 | Find the angle between vectors $ \left(0.866,~\dfrac{ 1 }{ 2 }\right)$ and $\left(-0.7071,~-0.7071\right)$. | 2 |
1006 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(3,~-6\right) $ . | 2 |
1007 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-3\right) $ . | 2 |
1008 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~6\right) $ . | 2 |
1009 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~9\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ . | 2 |
1010 | Find the sum of the vectors $ \vec{v_1} = \left(-12,~9\right) $ and $ \vec{v_2} = \left(-5,~-4\right) $ . | 2 |
1011 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 23 }{ 20 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 41 }{ 20 },~0\right) $ . | 2 |
1012 | Find the sum of the vectors $ \vec{v_1} = \left(12,~12\right) $ and $ \vec{v_2} = \left(-5,~\dfrac{ 9 }{ 2 }\right) $ . | 2 |
1013 | Find the angle between vectors $ \left(7,~2\right)$ and $\left(21,~6\right)$. | 2 |
1014 | Find the projection of the vector $ \vec{v_1} = \left(33.3793,~536.4621\right) $ on the vector $ \vec{v_2} = \left(44.7848,~528.8015\right) $. | 2 |
1015 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~8\right) $ . | 2 |
1016 | Find the magnitude of the vector $ \| \vec{v} \| = \left(30,~12\right) $ . | 2 |
1017 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 2 |
1018 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~2\right) $ and $ \vec{v_2} = \left(-1,~5,~-2\right) $ . | 2 |
1019 | Find the projection of the vector $ \vec{v_1} = \left(-5,~-1\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 2 |
1020 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-2\right) $ . | 2 |
1021 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 2069 }{ 100 },~\dfrac{ 857 }{ 100 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 997 }{ 100 },~\dfrac{ 1499 }{ 50 }\right) $ . | 2 |
1022 | Find the angle between vectors $ \left(12,~11,~5\right)$ and $\left(4,~15,~5\right)$. | 2 |
1023 | Find the angle between vectors $ \left(3,~-5\right)$ and $\left(6,~-10\right)$. | 2 |
1024 | Find the difference of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(14,~18\right) $ . | 2 |
1025 | Find the angle between vectors $ \left(-5,~3\right)$ and $\left(2,~6\right)$. | 2 |
1026 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-6\right) $ . | 2 |
1027 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~1\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ . | 2 |
1028 | Find the angle between vectors $ \left(-4,~3\right)$ and $\left(3,~8\right)$. | 2 |
1029 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 2 |
1030 | Find the magnitude of the vector $ \| \vec{v} \| = \left(150,~30\right) $ . | 2 |
1031 | Find the sum of the vectors $ \vec{v_1} = \left(5,~16\right) $ and $ \vec{v_2} = \left(8,~4\right) $ . | 2 |
1032 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 2 |
1033 | Find the angle between vectors $ \left(2,~3\right)$ and $\left(-3,~-2\right)$. | 2 |
1034 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 2 |
1035 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-5,~4\right) $ . | 2 |
1036 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-3\right) $ and $ \vec{v_2} = \left(-7,~5\right) $ . | 2 |
1037 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~5\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ . | 2 |
1038 | Find the angle between vectors $ \left(0,~2,~14\right)$ and $\left(0,~-2,~10\right)$. | 2 |
1039 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-5\right) $ . | 2 |
1040 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~-21\right) $ . | 2 |
1041 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1\right) $ . | 2 |
1042 | Find the angle between vectors $ \left(4,~-1\right)$ and $\left(3,~2\right)$. | 2 |
1043 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 2 |
1044 | Find the angle between vectors $ \left(-3,~8\right)$ and $\left(4,~12\right)$. | 2 |
1045 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~8\right) $ . | 2 |
1046 | Find the sum of the vectors $ \vec{v_1} = \left(10,~1\right) $ and $ \vec{v_2} = \left(1,~10\right) $ . | 2 |
1047 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 2 |
1048 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~-15\right) $ and $ \vec{v_2} = \left(14,~8\right) $ . | 2 |
1049 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 7 }{ 5 },~\dfrac{ 7 }{ 5 }\right) $ . | 2 |
1050 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 8 },~\dfrac{ 7 }{ 8 }\right) $ and $ \vec{v_2} = \left(8,~22\right) $ . | 2 |