Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1051 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(0,~9\right) $ . | 2 |
1052 | Find the difference of the vectors $ \vec{v_1} = \left(250,~40\right) $ and $ \vec{v_2} = \left(-110,~282\right) $ . | 2 |
1053 | Find the projection of the vector $ \vec{v_1} = \left(1,~-1\right) $ on the vector $ \vec{v_2} = \left(-3,~-2\right) $. | 2 |
1054 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 2 |
1055 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-8,~4\right) $ . | 2 |
1056 | Find the magnitude of the vector $ \| \vec{v} \| = \left(32,~-24\right) $ . | 2 |
1057 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-6\right) $ . | 2 |
1058 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-6\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ . | 2 |
1059 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~0\right) $ . | 2 |
1060 | Find the projection of the vector $ \vec{v_1} = \left(2,~-5\right) $ on the vector $ \vec{v_2} = \left(5,~1\right) $. | 2 |
1061 | Find the difference of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-3,~-7\right) $ . | 2 |
1062 | Find the angle between vectors $ \left(-4,~2,~-5\right)$ and $\left(1,~1,~3\right)$. | 2 |
1063 | Find the difference of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(3,~3 \sqrt{ 3 }\right) $ . | 2 |
1064 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 8 }{ 9 },~-\dfrac{ 40 }{ 9 }\right) $ and $ \vec{v_2} = \left(6,~56\right) $ . | 2 |
1065 | Find the angle between vectors $ \left(7,~8\right)$ and $\left(5,~-3\right)$. | 2 |
1066 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(2,~8\right) $ . | 2 |
1067 | Find the angle between vectors $ \left(3,~8\right)$ and $\left(-2,~\dfrac{ 3 }{ 2 }\right)$. | 2 |
1068 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~6,~2\right) $ and $ \vec{v_2} = \left(2,~3,~0\right) $ . | 2 |
1069 | Find the angle between vectors $ \left(3,~22\right)$ and $\left(7,~-3\right)$. | 2 |
1070 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-5\right) $ and $ \vec{v_2} = \left(-4,~5\right) $ . | 2 |
1071 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(\sqrt{ 3 },~3\right) $ . | 2 |
1072 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~-4\right) $ . | 2 |
1073 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~3\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 2 |
1074 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 2 |
1075 | Find the projection of the vector $ \vec{v_1} = \left(2,~1\right) $ on the vector $ \vec{v_2} = \left(-3,~4\right) $. | 2 |
1076 | Find the sum of the vectors $ \vec{v_1} = \left(8,~6\right) $ and $ \vec{v_2} = \left(-8,~5\right) $ . | 2 |
1077 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 7 }{ 5 },~\dfrac{ 7 }{ 5 }\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ . | 2 |
1078 | Find the projection of the vector $ \vec{v_1} = \left(6,~0\right) $ on the vector $ \vec{v_2} = \left(3,~3 \sqrt{ 3 }\right) $. | 2 |
1079 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(-8,~7\right)$. | 2 |
1080 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~0\right) $ and $ \vec{v_2} = \left(9,~9\right) $ . | 2 |
1081 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 50 },~\dfrac{ 3 }{ 40 },~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 433 }{ 2 },~125\right) $ . | 2 |
1082 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~6\right) $ and $ \vec{v_2} = \left(-5,~9\right) $ . | 2 |
1083 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(0,~1\right) $ are linearly independent or dependent. | 2 |
1084 | Find the projection of the vector $ \vec{v_1} = \left(1,~-2,~1\right) $ on the vector $ \vec{v_2} = \left(4,~-4,~7\right) $. | 2 |
1085 | Find the sum of the vectors $ \vec{v_1} = \left(7,~8\right) $ and $ \vec{v_2} = \left(9,~0\right) $ . | 2 |
1086 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-3\right) $ . | 2 |
1087 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(4,~4\right) $ . | 2 |
1088 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(-3,~-8\right) $ . | 2 |
1089 | Find the projection of the vector $ \vec{v_1} = \left(1,~8\right) $ on the vector $ \vec{v_2} = \left(-3,~-4\right) $. | 2 |
1090 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-3\right) $ and $ \vec{v_2} = \left(-2,~-3\right) $ . | 2 |
1091 | Find the difference of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 2 |
1092 | Find the angle between vectors $ \left(3,~0\right)$ and $\left(9,~9\right)$. | 2 |
1093 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 2 |
1094 | Find the projection of the vector $ \vec{v_1} = \left(2 \sqrt{ 3 },~2\right) $ on the vector $ \vec{v_2} = \left(6,~0\right) $. | 2 |
1095 | Find the sum of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(9,~0\right) $ . | 2 |
1096 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 2 |
1097 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~5\right) $ . | 2 |
1098 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 2 |
1099 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2 \sqrt{ 3 }\right) $ . | 2 |
1100 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~5,~5\right) $ and $ \vec{v_2} = \left(5,~0,~-5\right) $ . | 2 |