Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
201 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~7\right) $ . | 3 |
202 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~1\right) $ . | 3 |
203 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~3\right) $ . | 3 |
204 | Find the sum of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 3 |
205 | Find the difference of the vectors $ \vec{v_1} = \left(3,~11\right) $ and $ \vec{v_2} = \left(-4,~10\right) $ . | 3 |
206 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~3\right) $ . | 3 |
207 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-5\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 3 |
208 | Find the sum of the vectors $ \vec{v_1} = \left(-24,~4\right) $ and $ \vec{v_2} = \left(13,~14\right) $ . | 3 |
209 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 21 }{ 10 },~-\dfrac{ 16 }{ 5 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 3 |
210 | Find the sum of the vectors $ \vec{v_1} = \left(37.8,~39.6\right) $ and $ \vec{v_2} = \left(4.73,~-4.99\right) $ . | 3 |
211 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~0\right) $ . | 3 |
212 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 3 |
213 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-2\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 3 |
214 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 39 }{ 10 },~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 3 |
215 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ . | 3 |
216 | Find the difference of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(0,~15\right) $ . | 3 |
217 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-1\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 3 |
218 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(-4,~-6\right) $ . | 3 |
219 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 3 |
220 | Find the projection of the vector $ \vec{v_1} = \left(0,~-5,~7\right) $ on the vector $ \vec{v_2} = \left(-5,~1,~5\right) $. | 3 |
221 | Find the sum of the vectors $ \vec{v_1} = \left(-36,~4\right) $ and $ \vec{v_2} = \left(21,~13\right) $ . | 3 |
222 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~1\right) $ and $ \vec{v_2} = \left(11,~15\right) $ . | 3 |
223 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~7\right) $ . | 3 |
224 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-2,~-2\right) $ . | 3 |
225 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~11\right) $ and $ \vec{v_2} = \left(10,~4\right) $ . | 3 |
226 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~3\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ . | 3 |
227 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~7\right) $ . | 3 |
228 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0\right) $ . | 3 |
229 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-12\right) $ and $ \vec{v_2} = \left(-12,~-15\right) $ . | 3 |
230 | Find the angle between vectors $ \left(-5,~2\right)$ and $\left(10,~4\right)$. | 3 |
231 | Find the angle between vectors $ \left(8,~5\right)$ and $\left(5,~-8\right)$. | 3 |
232 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(3,~-3\right) $ . | 3 |
233 | Find the difference of the vectors $ \vec{v_1} = \left(10,~3\right) $ and $ \vec{v_2} = \left(4,~8\right) $ . | 3 |
234 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-2,~4\right) $ and $ \vec{v_2} = \left(0,~-3,~3\right) $ . | 3 |
235 | Find the difference of the vectors $ \vec{v_1} = \left(8,~2\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ . | 3 |
236 | Find the sum of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(10,~-120\right) $ . | 3 |
237 | Find the angle between vectors $ \left(-10,~5\right)$ and $\left(-9,~-10\right)$. | 3 |
238 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 3 |
239 | Find the angle between vectors $ \left(-2,~-7\right)$ and $\left(5,~-9\right)$. | 3 |
240 | Determine whether the vectors $ \vec{v_1} = \left(-\sqrt{ 160 },~\sqrt{ 40 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 6 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ are linearly independent or dependent. | 3 |
241 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-4\right) $ . | 3 |
242 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2\right) $ . | 3 |
243 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3\right) $ . | 3 |
244 | Determine whether the vectors $ \vec{v_1} = \left(4,~5,~7\right) $, $ \vec{v_2} = \left(6,~7,~6\right) $ and $ \vec{v_3} = \left(-4,~-7,~3\right)$ are linearly independent or dependent. | 3 |
245 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-2\right) $ . | 3 |
246 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~1\right) $ and $ \vec{v_2} = \left(4,~3,~-1\right) $ . | 3 |
247 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~5\right) $ . | 3 |
248 | Find the angle between vectors $ \left(0,~2,~14\right)$ and $\left(0,~2,~-10\right)$. | 3 |
249 | Determine whether the vectors $ \vec{v_1} = \left(2,~-8,~8\right) $, $ \vec{v_2} = \left(16,~-72,~71\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 3 |
250 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-4\right) $ . | 3 |