Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2301 | Find the angle between vectors $ \left(1,~2\right)$ and $\left(-6,~3\right)$. | 2 |
2302 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~5\right) $ and $ \vec{v_2} = \left(-2,~-1,~4\right) $ . | 2 |
2303 | Find the angle between vectors $ \left(2,~2\right)$ and $\left(4,~-5\right)$. | 2 |
2304 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 71 }{ 1000 },~\dfrac{ 833 }{ 1000 },~\dfrac{ 137 }{ 200 }\right) $ . | 2 |
2305 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 4 }\right) $ . | 2 |
2306 | Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(2,~6\right) $ . | 2 |
2307 | Find the angle between vectors $ \left(0,~5\right)$ and $\left(6,~6\right)$. | 2 |
2308 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 9 }{ 7 },~0\right) $ . | 2 |
2309 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(-2,~-1\right)$. | 2 |
2310 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ . | 2 |
2311 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~3\right) $ . | 2 |
2312 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0\right) $ . | 2 |
2313 | Find the difference of the vectors $ \vec{v_1} = \left(-27,~24\right) $ and $ \vec{v_2} = \left(-5,~-40\right) $ . | 2 |
2314 | Determine whether the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(-23,~9\right) $ are linearly independent or dependent. | 2 |
2315 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~3,~2\right) $ and $ \vec{v_2} = \left(1,~3,~1\right) $ . | 2 |
2316 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~13\right) $ . | 2 |
2317 | Find the angle between vectors $ \left(2,~0\right)$ and $\left(2,~8\right)$. | 2 |
2318 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~8\right) $ . | 2 |
2319 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 3 }{ 20 },~\dfrac{ 1 }{ 5 }\right) $ . | 2 |
2320 | Determine whether the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ are linearly independent or dependent. | 2 |
2321 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 2 |
2322 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~-4\right) $ and $ \vec{v_2} = \left(-3,~-4,~-5\right) $ . | 2 |
2323 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ . | 2 |
2324 | Find the angle between vectors $ \left(2,~0\right)$ and $\left(1,~1\right)$. | 2 |
2325 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 2 |
2326 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 329 }{ 10 },~\dfrac{ 189 }{ 10 }\right) $ . | 2 |
2327 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~-2\right) $ and $ \vec{v_2} = \left(4,~1,~1\right) $ . | 2 |
2328 | Find the difference of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 2 |
2329 | Find the sum of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 2 |
2330 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-4\right) $ . | 2 |
2331 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-4\right) $ . | 2 |
2332 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-4\right) $ and $ \vec{v_2} = \left(4,~-5,~6\right) $ . | 2 |
2333 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 2 |
2334 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(5,~-2\right)$. | 2 |
2335 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-12\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 4 }{ 5 }\right) $ . | 2 |
2336 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(7,~1\right) $ . | 2 |
2337 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-7\right) $ and $ \vec{v_2} = \left(5,~9\right) $ . | 2 |
2338 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~8\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 2 |
2339 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~-5\right) $ and $ \vec{v_2} = \left(4,~9\right) $ . | 2 |
2340 | Find the angle between vectors $ \left(4,~4\right)$ and $\left(-4,~4\right)$. | 2 |
2341 | Find the difference of the vectors $ \vec{v_1} = \left(6,~9,~3\right) $ and $ \vec{v_2} = \left(1,~3,~0\right) $ . | 2 |
2342 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(9,~-8\right) $ . | 2 |
2343 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~0\right) $ . | 2 |
2344 | Calculate the dot product 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 |
2345 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(6,~4\right) $ . | 2 |
2346 | Find the difference of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 2 |
2347 | Find the projection of the vector $ \vec{v_1} = \left(2,~-7\right) $ on the vector $ \vec{v_2} = \left(5,~9\right) $. | 2 |
2348 | Find the angle between vectors $ \left(-2,~8\right)$ and $\left(4,~-3\right)$. | 2 |
2349 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~-2\right) $ and $ \vec{v_2} = \left(5,~0,~-5\right) $ . | 2 |
2350 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 2 |