Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6151 | Calculate the dot product of the vectors $ \vec{v_1} = \left(210,~310\right) $ and $ \vec{v_2} = \left(\dfrac{ 27 }{ 10 },~\dfrac{ 291 }{ 100 }\right) $ . | 1 |
6152 | Find the difference of the vectors $ \vec{v_1} = \left(8,~-1\right) $ and $ \vec{v_2} = \left(-3,~0\right) $ . | 1 |
6153 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-12,~2\right) $ and $ \vec{v_2} = \left(1,~6\right) $ . | 1 |
6154 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-4,~0\right) $ and $ \vec{v_2} = \left(6,~-5,~2\right) $ . | 1 |
6155 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~3,~-1\right) $ . | 1 |
6156 | Find the projection of the vector $ \vec{v_1} = \left(-48,~-25,~20\right) $ on the vector $ \vec{v_2} = \left(60,~30,~40\right) $. | 1 |
6157 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~3,~3\right) $ and $ \vec{v_2} = \left(3,~-1,~2\right) $ . | 1 |
6158 | Find the angle between vectors $ \left(5,~3\right)$ and $\left(8,~9\right)$. | 1 |
6159 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2,~8\right) $ and $ \vec{v_2} = \left(3,~2,~-1\right) $ . | 1 |
6160 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-2,~0,~1\right) $ . | 1 |
6161 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(1,~3,~-5\right) $ . | 1 |
6162 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(2,~-9\right) $ . | 1 |
6163 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~2,~-1\right) $ . | 1 |
6164 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-1,~-1\right) $ . | 1 |
6165 | Find the angle between vectors $ \left(50,~105\right)$ and $\left(64,~130\right)$. | 1 |
6166 | Find the angle between vectors $ \left(\sqrt{ 3 },~4,~-1\right)$ and $\left(1,~-4,~\sqrt{ 3 }\right)$. | 1 |
6167 | Determine whether the vectors $ \vec{v_1} = \left(2,~5,~7\right) $, $ \vec{v_2} = \left(4,~-1,~3\right) $ and $ \vec{v_3} = \left(10,~8,~-9\right)$ are linearly independent or dependent. | 1 |
6168 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~2\right) $ and $ \vec{v_2} = \left(-1,~7,~2\right) $ . | 1 |
6169 | Find the angle between vectors $ \left(15,~-18\right)$ and $\left(19,~40\right)$. | 1 |
6170 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~7\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
6171 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-2,~2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
6172 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-4,~1\right) $ . | 1 |
6173 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-2\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ . | 1 |
6174 | Find the angle between vectors $ \left(-15,~-8\right)$ and $\left(-2,~3\right)$. | 1 |
6175 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(6,~-2\right) $ . | 1 |
6176 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2,~8\right) $ and $ \vec{v_2} = \left(3,~-2,~1\right) $ . | 1 |
6177 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~30\right) $ . | 1 |
6178 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-1,~2\right) $ . | 1 |
6179 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~1,~5\right) $ and $ \vec{v_2} = \left(2,~3,~2\right) $ . | 1 |
6180 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~2,~-4\right) $ and $ \vec{v_2} = \left(1,~1,~-6\right) $ . | 1 |
6181 | Find the sum of the vectors $ \vec{v_1} = \left(-242.8106,~-129.1047\right) $ and $ \vec{v_2} = \left(-\dfrac{ 153909 }{ 10000 },~\dfrac{ 422861 }{ 10000 }\right) $ . | 1 |
6182 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~-3\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 1 |
6183 | Find the angle between vectors $ \left(3,~6,~-2\right)$ and $\left(2,~-2,~1\right)$. | 1 |
6184 | Find the angle between vectors $ \left(1,~3,~-1\right)$ and $\left(-3,~-9,~3\right)$. | 1 |
6185 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(1,~1\right)$. | 1 |
6186 | Determine whether the vectors $ \vec{v_1} = \left(1,~3,~0\right) $, $ \vec{v_2} = \left(-2,~0,~1\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
6187 | Find the projection of the vector $ \vec{v_1} = \left(40,~-30\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 1 |
6188 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 1 |
6189 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~8\right) $ and $ \vec{v_2} = \left(-1,~-8\right) $ . | 1 |
6190 | Find the difference of the vectors $ \vec{v_1} = \left(-48,~-25,~20\right) $ and $ \vec{v_2} = \left(60,~30,~40\right) $ . | 1 |
6191 | Find the angle between vectors $ \left(-5,~7\right)$ and $\left(-6,~-4\right)$. | 1 |
6192 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~2\right) $ . | 1 |
6193 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2,~8\right) $ and $ \vec{v_2} = \left(1,~2,~1\right) $ . | 1 |
6194 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 1 |
6195 | Find the angle between vectors $ \left(5,~1,~0\right)$ and $\left(-11,~-11,~-8\right)$. | 1 |
6196 | Find the sum of the vectors $ \vec{v_1} = \left(-9,~2\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ . | 1 |
6197 | Find the projection of the vector $ \vec{v_1} = \left(2,~3,~2\right) $ on the vector $ \vec{v_2} = \left(4,~1,~5\right) $. | 1 |
6198 | Find the angle between vectors $ \left(1,~0,~1\right)$ and $\left(1,~1,~0\right)$. | 1 |
6199 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4,~-1\right) $ and $ \vec{v_2} = \left(-3,~-4,~-3\right) $ . | 1 |
6200 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-3,~-9\right) $ and $ \vec{v_2} = \left(-13,~-11,~5\right) $ . | 1 |