Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
951 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~1\right) $ . | 2 |
952 | Find the angle between vectors $ \left(-4,~6\right)$ and $\left(2,~-1\right)$. | 2 |
953 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 2 |
954 | Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(2,~5\right) $. | 2 |
955 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 2 |
956 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-4,~2\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 2 |
957 | Determine whether the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~2\right) $ are linearly independent or dependent. | 2 |
958 | Determine whether the vectors $ \vec{v_1} = \left(-1,~-4,~-7\right) $, $ \vec{v_2} = \left(3,~8,~-1\right) $ and $ \vec{v_3} = \left(2,~-6,~-59\right)$ are linearly independent or dependent. | 2 |
959 | Find the sum of the vectors $ \vec{v_1} = \left(6,~3\right) $ and $ \vec{v_2} = \left(7,~-15\right) $ . | 2 |
960 | Determine whether the vectors $ \vec{v_1} = \left(-5,~-4\right) $ and $ \vec{v_2} = \left(-2,~\dfrac{ 1 }{ 4 }\right) $ are linearly independent or dependent. | 2 |
961 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 63961 }{ 125 },~\dfrac{ 35737 }{ 2000 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 304999 }{ 1000 },~-\dfrac{ 44319 }{ 200 }\right) $ . | 2 |
962 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~1\right) $ . | 2 |
963 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 2 |
964 | Find the difference of the vectors $ \vec{v_1} = \left(-16,~12\right) $ and $ \vec{v_2} = \left(-10,~0\right) $ . | 2 |
965 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~8\right) $ and $ \vec{v_2} = \left(7,~5\right) $ . | 2 |
966 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(1,~-2\right)$. | 2 |
967 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-5\right) $ and $ \vec{v_2} = \left(6,~5\right) $ . | 2 |
968 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 2 |
969 | Find the difference of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(-9,~16\right) $ . | 2 |
970 | Find the angle between vectors $ \left(-4,~1\right)$ and $\left(-5,~2\right)$. | 2 |
971 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-6\right) $ and $ \vec{v_2} = \left(9,~-3\right) $ . | 2 |
972 | Find the angle between vectors $ \left(-1,~2\right)$ and $\left(1,~4\right)$. | 2 |
973 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-4\right) $ and $ \vec{v_2} = \left(-3,~8\right) $ . | 2 |
974 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 2 |
975 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ . | 2 |
976 | Find the difference of the vectors $ \vec{v_1} = \left(7,~4\right) $ and $ \vec{v_2} = \left(-9,~28\right) $ . | 2 |
977 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~3,~1\right) $ . | 2 |
978 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ . | 2 |
979 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(6,~-8,~3\right) $ . | 2 |
980 | Find the magnitude of the vector $ \| \vec{v} \| = \left(15,~7\right) $ . | 2 |
981 | Find the angle between vectors $ \left(\dfrac{ 26 }{ 5 },~-\dfrac{ 43 }{ 10 }\right)$ and $\left(-\dfrac{ 71 }{ 10 },~-\dfrac{ 16 }{ 5 }\right)$. | 2 |
982 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2\right) $ . | 2 |
983 | Find the difference of the vectors $ \vec{v_1} = \left(190,~60\right) $ and $ \vec{v_2} = \left(-120,~296\right) $ . | 2 |
984 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(-7,~6\right) $ . | 2 |
985 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~11 \sqrt{ 3 }\right) $ . | 2 |
986 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~0\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 2 |
987 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-1\right) $ . | 2 |
988 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(15,~9\right) $ . | 2 |
989 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 2 |
990 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-13,~-7\right) $ . | 2 |
991 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~2\right) $ . | 2 |
992 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-15,~0,~20\right) $ and $ \vec{v_2} = \left(0,~50,~0\right) $ . | 2 |
993 | Find the sum of the vectors $ \vec{v_1} = \left(-48,~64\right) $ and $ \vec{v_2} = \left(54,~27\right) $ . | 2 |
994 | Find the projection of the vector $ \vec{v_1} = \left(2,~1\right) $ on the vector $ \vec{v_2} = \left(1,~2\right) $. | 2 |
995 | Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~8\right) $ and $ \vec{v_2} = \left(-10,~-9\right) $ . | 2 |
996 | Determine whether the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(2,~3\right) $ are linearly independent or dependent. | 2 |
997 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(1,~-2,~3\right) $ . | 2 |
998 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-8\right) $ . | 2 |
999 | Calculate the dot product of the vectors $ \vec{v_1} = \left(33.3793,~536.4621\right) $ and $ \vec{v_2} = \left(44.7848,~528.8015\right) $ . | 2 |
1000 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 25 }{ 4 },~-\dfrac{ 19 }{ 5 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 23 }{ 5 },~\dfrac{ 11 }{ 4 }\right) $ . | 2 |