Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
1151 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-3,~6\right) $ . | 2 |
1152 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~-3\right) $ . | 2 |
1153 | Find the projection of the vector $ \vec{v_1} = \left(0,~4\right) $ on the vector $ \vec{v_2} = \left(-1,~-3\right) $. | 2 |
1154 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-11,~-5\right) $ . | 2 |
1155 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0\right) $ . | 2 |
1156 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 61 }{ 10 },~\dfrac{ 17 }{ 2 }\right) $ and $ \vec{v_2} = \left(-5,~\dfrac{ 9 }{ 2 }\right) $ . | 2 |
1157 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(1,~2\right)$. | 2 |
1158 | Find the projection of the vector $ \vec{v_1} = \left(7,~7\right) $ on the vector $ \vec{v_2} = \left(-8,~5\right) $. | 2 |
1159 | Find the difference of the vectors $ \vec{v_1} = \left(225,~10\right) $ and $ \vec{v_2} = \left(-150,~285\right) $ . | 2 |
1160 | Find the difference of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(2,~-4\right) $ . | 2 |
1161 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~3,~-4\right) $ and $ \vec{v_2} = \left(-2,~3,~-7\right) $ . | 2 |
1162 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-12\right) $ . | 2 |
1163 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-1\right) $ and $ \vec{v_2} = \left(4,~-8\right) $ . | 2 |
1164 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~-1,~0\right) $ . | 2 |
1165 | Find the difference of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 2 |
1166 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 2 |
1167 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 5 }{ 13 },~\dfrac{ 12 }{ 13 }\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ . | 2 |
1168 | Find the projection of the vector $ \vec{v_1} = \left(0,~0,~0\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $. | 2 |
1169 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~6\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 2 |
1170 | Find the angle between vectors $ \left(5,~6\right)$ and $\left(-1,~4\right)$. | 2 |
1171 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~8\right) $ . | 2 |
1172 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 83 }{ 10 },~3\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 5 },~\dfrac{ 34 }{ 5 }\right) $ . | 2 |
1173 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~2\right) $ and $ \vec{v_2} = \left(16,~12\right) $ . | 2 |
1174 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(3,~28\right) $ . | 2 |
1175 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 83 }{ 10 },~3\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 5 },~\dfrac{ 34 }{ 5 }\right) $ . | 2 |
1176 | Find the angle between vectors $ \left(\dfrac{ 5 }{ 13 },~\dfrac{ 12 }{ 13 }\right)$ and $\left(-4,~8\right)$. | 2 |
1177 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~7\right) $ and $ \vec{v_2} = \left(-6,~3\right) $ . | 2 |
1178 | Find the projection of the vector $ \vec{v_1} = \left(-2,~0,~-3\right) $ on the vector $ \vec{v_2} = \left(1,~-3,~-1\right) $. | 2 |
1179 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~2\right) $ . | 2 |
1180 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-6\right) $ . | 2 |
1181 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~4\right) $ and $ \vec{v_2} = \left(-3,~6\right) $ . | 2 |
1182 | Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(-7,~2\right) $ . | 2 |
1183 | Find the angle between vectors $ \left(-2,~3,~1\right)$ and $\left(1,~1,~2\right)$. | 2 |
1184 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ . | 2 |
1185 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-5\right) $ . | 2 |
1186 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(-4,~12\right) $ . | 2 |
1187 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~10\right) $ . | 2 |
1188 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~\dfrac{ 9 }{ 2 },~2\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 13 }{ 5 },~\dfrac{ 13 }{ 5 }\right) $ . | 2 |
1189 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\sqrt{ 2 },~-\dfrac{ 1 }{ 2 }\right) $ . | 2 |
1190 | Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(7,~2\right) $ . | 2 |
1191 | Find the sum of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 2 |
1192 | Find the angle between vectors $ \left(-6,~4\right)$ and $\left(3,~3\right)$. | 2 |
1193 | Find the angle between vectors $ \left(-4,~-3\right)$ and $\left(-1,~3\right)$. | 2 |
1194 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-2\right) $ . | 2 |
1195 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ . | 2 |
1196 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 173 }{ 10 },~10\right) $ and $ \vec{v_2} = \left(-\dfrac{ 63 }{ 10 },~\dfrac{ 68 }{ 5 }\right) $ . | 2 |
1197 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-24,~-7\right) $ . | 2 |
1198 | Find the projection of the vector $ \vec{v_1} = \left(8,~150\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 2 |
1199 | Find the angle between vectors $ \left(-6,~4\right)$ and $\left(-3,~6\right)$. | 2 |
1200 | Find the sum of the vectors $ \vec{v_1} = \left(0,~75\right) $ and $ \vec{v_2} = \left(250,~75\right) $ . | 2 |