Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2251 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(4,~26\right) $ . | 2 |
2252 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~9\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 2 |
2253 | Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(0,~3\right) $ . | 2 |
2254 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~3\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 2 |
2255 | Determine whether the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ are linearly independent or dependent. | 2 |
2256 | Find the angle between vectors $ \left(8,~6\right)$ and $\left(3,~-4\right)$. | 2 |
2257 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 2 |
2258 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0,~7\right) $ . | 2 |
2259 | Calculate the dot product of the vectors $ \vec{v_1} = \left(89,~157\right) $ and $ \vec{v_2} = \left(237,~326\right) $ . | 2 |
2260 | Find the sum of the vectors $ \vec{v_1} = \left(4,~0\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 2 |
2261 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(3,~3\right) $ . | 2 |
2262 | Find the angle between vectors $ \left(1,~-\sqrt{ 3 },~\dfrac{ 3 }{ 2 }\right)$ and $\left(\sqrt{ 2 },~1,~\dfrac{ 2 }{ 3 }\right)$. | 2 |
2263 | Find the angle between vectors $ \left(1,~-4\right)$ and $\left(-2,~0\right)$. | 2 |
2264 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 2 |
2265 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-2\right) $ . | 2 |
2266 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 8 }{ 17 },~\dfrac{ 15 }{ 17 }\right) $ . | 2 |
2267 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~25\right) $ . | 2 |
2268 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~13\right) $ . | 2 |
2269 | Find the sum of the vectors $ \vec{v_1} = \left(1,~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 2 |
2270 | Find the sum of the vectors $ \vec{v_1} = \left(4,~7\right) $ and $ \vec{v_2} = \left(8,~9\right) $ . | 2 |
2271 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~3\right) $ . | 2 |
2272 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(2,~-1\right)$. | 2 |
2273 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-23\right) $ . | 2 |
2274 | Find the angle between vectors $ \left(2,~0\right)$ and $\left(-2,~-1\right)$. | 2 |
2275 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ . | 2 |
2276 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(1,~-3\right)$. | 2 |
2277 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~8,~9\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 2 |
2278 | Find the angle between vectors $ \left(2 \sqrt{ 3 },~\sqrt{ 3 },~-1\right)$ and $\left(1,~-2,~2\right)$. | 2 |
2279 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~\dfrac{ 1 }{ 2 }\right) $ . | 2 |
2280 | Find the magnitude of the vector $ \| \vec{v} \| = \left(13,~5\right) $ . | 2 |
2281 | Find the projection of the vector $ \vec{v_1} = \left(-2,~0\right) $ on the vector $ \vec{v_2} = \left(3,~0\right) $. | 2 |
2282 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 2 |
2283 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 333 }{ 100 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 333 }{ 100 },~120\right) $ . | 2 |
2284 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~7\right) $ . | 2 |
2285 | Find the projection of the vector $ \vec{v_1} = \left(2,~-1\right) $ on the vector $ \vec{v_2} = \left(-1,~3\right) $. | 2 |
2286 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2\right) $ . | 2 |
2287 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~3\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 2 |
2288 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~9\right) $ . | 2 |
2289 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 2 |
2290 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 333 }{ 100 },~0\right) $ . | 2 |
2291 | Find the angle between vectors $ \left(-6,~13\right)$ and $\left(1,~0\right)$. | 2 |
2292 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(-1,~3\right)$. | 2 |
2293 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ . | 2 |
2294 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2\right) $ . | 2 |
2295 | Find the angle between vectors $ \left(7,~4\right)$ and $\left(7,~4\right)$. | 2 |
2296 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~3\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 2 |
2297 | Find the difference of the vectors $ \vec{v_1} = \left(-27,~24\right) $ and $ \vec{v_2} = \left(5,~-40\right) $ . | 2 |
2298 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-7\right) $ and $ \vec{v_2} = \left(-11,~-4\right) $ . | 2 |
2299 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ . | 2 |
2300 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 333 }{ 100 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 333 }{ 100 },~120\right) $ . | 2 |