Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2201 | Find the angle between vectors $ \left(61,~39\right)$ and $\left(24,~1\right)$. | 2 |
2202 | Find the sum of the vectors $ \vec{v_1} = \left(8,~7\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ . | 2 |
2203 | Find the angle between vectors $ \left(-3,~-4\right)$ and $\left(6,~-8\right)$. | 2 |
2204 | Find the angle between vectors $ \left(1,~0\right)$ and $\left(0,~1\right)$. | 2 |
2205 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~12\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ . | 2 |
2206 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-7\right) $ and $ \vec{v_2} = \left(-2,~6\right) $ . | 2 |
2207 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(0,~2\right) $ . | 2 |
2208 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1\right) $ . | 2 |
2209 | Find the angle between vectors $ \left(-1,~0\right)$ and $\left(-4,~0\right)$. | 2 |
2210 | Find the sum of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 2 |
2211 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~48\right) $ . | 2 |
2212 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ are linearly independent or dependent. | 2 |
2213 | Find the sum of the vectors $ \vec{v_1} = \left(4,~0\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 2 |
2214 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 2 |
2215 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(5,~7\right) $ . | 2 |
2216 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1\right) $ . | 2 |
2217 | Find the difference of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 2 |
2218 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 8 }{ 17 },~\dfrac{ 15 }{ 17 }\right) $ . | 2 |
2219 | Find the angle between vectors $ \left(3,~-1\right)$ and $\left(3,~1\right)$. | 2 |
2220 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(4,~0\right) $ . | 2 |
2221 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
2222 | Find the sum of the vectors $ \vec{v_1} = \left(9,~8\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 2 |
2223 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-4\right) $ . | 2 |
2224 | Find the projection of the vector $ \vec{v_1} = \left(0,~1\right) $ on the vector $ \vec{v_2} = \left(2,~1\right) $. | 2 |
2225 | Find the angle between vectors $ \left(89,~157\right)$ and $\left(237,~326\right)$. | 2 |
2226 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ . | 2 |
2227 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-12\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~0\right) $ . | 2 |
2228 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-4\right) $ and $ \vec{v_2} = \left(-8,~9\right) $ . | 2 |
2229 | Find the magnitude of the vector $ \| \vec{v} \| = \left(110,~0\right) $ . | 2 |
2230 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 2 |
2231 | Find the angle between vectors $ \left(3,~-2,~4\right)$ and $\left(1,~-1,~5\right)$. | 2 |
2232 | Find the difference of the vectors $ \vec{v_1} = \left(240,~20\right) $ and $ \vec{v_2} = \left(-140,~305\right) $ . | 2 |
2233 | Find the difference of the vectors $ \vec{v_1} = \left(17537,~-\dfrac{ 35597 }{ 1000 }\right) $ and $ \vec{v_2} = \left(17432,~-\dfrac{ 38871 }{ 1000 }\right) $ . | 2 |
2234 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-1\right) $ . | 2 |
2235 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(-1,~-5\right) $ . | 2 |
2236 | Determine whether the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-6,~10\right) $ are linearly independent or dependent. | 2 |
2237 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-2\right) $ . | 2 |
2238 | Find the difference of the vectors $ \vec{v_1} = \left(89,~157\right) $ and $ \vec{v_2} = \left(237,~326\right) $ . | 2 |
2239 | Find the angle between vectors $ \left(1,~3\right)$ and $\left(-4,~10\right)$. | 2 |
2240 | Find the magnitude of the vector $ \| \vec{v} \| = \left(380,~-285\right) $ . | 2 |
2241 | Find the angle between vectors $ \left(56,~30\right)$ and $\left(25,~1\right)$. | 2 |
2242 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~4\right) $ and $ \vec{v_2} = \left(8,~-2\right) $ . | 2 |
2243 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 15 }{ 7 },~\dfrac{ 30 }{ 7 }\right) $ and $ \vec{v_2} = \left(10,~46\right) $ . | 2 |
2244 | Find the difference of the vectors $ \vec{v_1} = \left(5,~9\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 2 |
2245 | Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(3,~0\right) $ . | 2 |
2246 | Find the sum of the vectors $ \vec{v_1} = \left(89,~157\right) $ and $ \vec{v_2} = \left(237,~326\right) $ . | 2 |
2247 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(-24,~40\right) $ . | 2 |
2248 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-\sqrt{ 3 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\sqrt{ 2 },~1,~\dfrac{ 2 }{ 3 }\right) $ . | 2 |
2249 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~1\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 2 |
2250 | Find the angle between vectors $ \left(3,~3\right)$ and $\left(-5,~-20\right)$. | 2 |