Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1101 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(7,~-8\right) $ . | 2 |
1102 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(-6,~5\right) $ . | 2 |
1103 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(5,~3\right) $ . | 2 |
1104 | Find the difference of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(9,~0\right) $ . | 2 |
1105 | Find the sum of the vectors $ \vec{v_1} = \left(6,~7\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 2 |
1106 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 2 },~2\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 2 },~-7\right) $ are linearly independent or dependent. | 2 |
1107 | Find the angle between vectors $ \left(9,~-3\right)$ and $\left(5,~3\right)$. | 2 |
1108 | Find the projection of the vector $ \vec{v_1} = \left(-2,~4\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 2 |
1109 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~5\right) $ . | 2 |
1110 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-3\right) $ . | 2 |
1111 | Find the projection of the vector $ \vec{v_1} = \left(-2,~6\right) $ on the vector $ \vec{v_2} = \left(-9,~-3\right) $. | 2 |
1112 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-2,~2\right) $ and $ \vec{v_2} = \left(-20,~8,~-8\right) $ . | 2 |
1113 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1275,~2500\right) $ and $ \vec{v_2} = \left(\dfrac{ 66 }{ 5 },~\dfrac{ 41 }{ 5 }\right) $ . | 2 |
1114 | Find the difference of the vectors $ \vec{v_1} = \left(240,~90\right) $ and $ \vec{v_2} = \left(-140,~354.29\right) $ . | 2 |
1115 | Determine whether the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(0,~0\right) $ are linearly independent or dependent. | 2 |
1116 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-8,~6\right) $ . | 2 |
1117 | Find the angle between vectors $ \left(6,~7\right)$ and $\left(6,~-7\right)$. | 2 |
1118 | Find the sum of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 2 |
1119 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-15,~-20\right) $ . | 2 |
1120 | Find the angle between vectors $ \left(7,~7\right)$ and $\left(-4,~7\right)$. | 2 |
1121 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 23 }{ 5 },~-\dfrac{ 41 }{ 5 },~\dfrac{ 49 }{ 5 }\right) $ and $ \vec{v_2} = \left(-9,~-\dfrac{ 33 }{ 10 },~\dfrac{ 22 }{ 5 }\right) $ . | 2 |
1122 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 2 |
1123 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~8\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 2 |
1124 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~6\right) $ . | 2 |
1125 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(9,~0\right) $ . | 2 |
1126 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 4 },~\dfrac{ 147 }{ 50 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 281 }{ 100 },~\dfrac{ 53 }{ 100 }\right) $ . | 2 |
1127 | Find the difference of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(3,~3\right) $ . | 2 |
1128 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 2 |
1129 | Find the angle between vectors $ \left(3,~0\right)$ and $\left(5,~5\right)$. | 2 |
1130 | Find the difference of the vectors $ \vec{v_1} = \left(18,~45\right) $ and $ \vec{v_2} = \left(18,~0\right) $ . | 2 |
1131 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 2 |
1132 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 2 |
1133 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~5\right) $ . | 2 |
1134 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-8\right) $ . | 2 |
1135 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~-2\right) $ and $ \vec{v_2} = \left(0,~2,~5\right) $ . | 2 |
1136 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(0,~1,~-1\right) $ . | 2 |
1137 | Find the projection of the vector $ \vec{v_1} = \left(1,~1\right) $ on the vector $ \vec{v_2} = \left(8,~3\right) $. | 2 |
1138 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(4,~-3\right)$. | 2 |
1139 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(4,~-7\right) $ . | 2 |
1140 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 5 },~-\dfrac{ 4 }{ 5 }\right) $ . | 2 |
1141 | Find the projection of the vector $ \vec{v_1} = \left(7.07,~7.07\right) $ on the vector $ \vec{v_2} = \left(2.99,~7.42\right) $. | 2 |
1142 | Find the angle between vectors $ \left(3,~9\right)$ and $\left(-9,~5\right)$. | 2 |
1143 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
1144 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 2 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(9,~26\right) $ . | 2 |
1145 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 61 }{ 10 },~\dfrac{ 17 }{ 2 }\right) $ . | 2 |
1146 | Find the projection of the vector $ \vec{v_1} = \left(-2,~9\right) $ on the vector $ \vec{v_2} = \left(-1,~2\right) $. | 2 |
1147 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 2 |
1148 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(8,~3\right) $ . | 2 |
1149 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(-8,~-3\right) $ . | 2 |
1150 | Find the angle between vectors $ \left(0,~10\right)$ and $\left(0,~15\right)$. | 2 |