Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6201 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-1\right) $ . | 1 |
6202 | Determine whether the vectors $ \vec{v_1} = \left(2,~0,~2\right) $, $ \vec{v_2} = \left(1,~0,~-2\right) $ and $ \vec{v_3} = \left(2,~0,~1\right)$ are linearly independent or dependent. | 1 |
6203 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~1,~-3\right) $ . | 1 |
6204 | Find the projection of the vector $ \vec{v_1} = \left(7,~0\right) $ on the vector $ \vec{v_2} = \left(6.9663,~0.6861\right) $. | 1 |
6205 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~3,~2\right) $ and $ \vec{v_2} = \left(5,~0,~-1\right) $ . | 1 |
6206 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~3\right) $ and $ \vec{v_2} = \left(0,~3,~3\right) $ . | 1 |
6207 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-1\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 1 |
6208 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~6,~-1\right) $ . | 1 |
6209 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~5\right) $ . | 1 |
6210 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-9,~3\right) $ . | 1 |
6211 | Find the angle between vectors $ \left(385,~167\right)$ and $\left(31,~187\right)$. | 1 |
6212 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(1,~1\right)$. | 1 |
6213 | Find the angle between vectors $ \left(-5,~1,~0\right)$ and $\left(3,~8,~9\right)$. | 1 |
6214 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-2,~1\right) $ . | 1 |
6215 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
6216 | Find the angle between vectors $ \left(-3,~4\right)$ and $\left(2,~3\right)$. | 1 |
6217 | Determine whether the vectors $ \vec{v_1} = \left(1,~-\sqrt{ 3 },~\dfrac{ 3 }{ 2 }\right) $, $ \vec{v_2} = \left(\sqrt{ 2 },~1,~\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
6218 | Find the difference of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(0,~2\right) $ . | 1 |
6219 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~1\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ . | 1 |
6220 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~9,~2\right) $ and $ \vec{v_2} = \left(-7,~9,~2\right) $ . | 1 |
6221 | Find the angle between vectors $ \left(2,~2,~3\right)$ and $\left(-5,~4,~3\right)$. | 1 |
6222 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~1\right) $ and $ \vec{v_2} = \left(1,~2,~1\right) $ . | 1 |
6223 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~7,~5\right) $ and $ \vec{v_2} = \left(1,~-2,~3\right) $ . | 1 |
6224 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-10,~11\right) $ . | 1 |
6225 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~2\right) $ and $ \vec{v_2} = \left(4,~1,~5\right) $ . | 1 |
6226 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-1\right) $ . | 1 |
6227 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5,~2\right) $ . | 1 |
6228 | Find the angle between vectors $ \left(1,~1,~0\right)$ and $\left(1,~2,~2\right)$. | 1 |
6229 | Find the projection of the vector $ \vec{v_1} = \left(-6,~0,~5\right) $ on the vector $ \vec{v_2} = \left(1,~3,~-3\right) $. | 1 |
6230 | 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 |
6231 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(1,~2\right)$. | 1 |
6232 | 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(-2,~\dfrac{ 7 }{ 2 },~7\right)$ are linearly independent or dependent. | 1 |
6233 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~-5\right) $ . | 1 |
6234 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~-2\right) $ and $ \vec{v_2} = \left(2,~-1,~2\right) $ . | 1 |
6235 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-2,~1\right) $ and $ \vec{v_2} = \left(1,~0,~3\right) $ . | 1 |
6236 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
6237 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~8\right) $ . | 1 |
6238 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~1,~7\right) $ and $ \vec{v_2} = \left(3,~5,~9\right) $ . | 1 |
6239 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
6240 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~0\right) $ . | 1 |
6241 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-5\right) $ . | 1 |
6242 | Find the difference of the vectors $ \vec{v_1} = \left(3,~5,~1\right) $ and $ \vec{v_2} = \left(-6,~5,~-2\right) $ . | 1 |
6243 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3,~1\right) $ . | 1 |
6244 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1,~2\right) $ . | 1 |
6245 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~-1,~5\right) $ . | 1 |
6246 | Find the angle between vectors $ \left(3,~-2,~1\right)$ and $\left(1,~2,~1\right)$. | 1 |
6247 | Find the angle between vectors $ \left(-11,~-11,~-8\right)$ and $\left(-16,~-12,~-8\right)$. | 1 |
6248 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(1,~6\right) $ . | 1 |
6249 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~5\right) $ . | 1 |
6250 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 46 }{ 17 },~\dfrac{ 80 }{ 17 }\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 1 |