Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
301 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~0\right) $ . | 3 |
302 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~5\right) $ . | 3 |
303 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~2\right) $ . | 3 |
304 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 2 },~-\dfrac{ 3 }{ 2 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~-\dfrac{ 1 }{ 2 },~2\right) $ . | 3 |
305 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 42 }{ 5 },~0\right) $ . | 3 |
306 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2\right) $ . | 3 |
307 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~2\right) $ and $ \vec{v_2} = \left(1,~1,~4\right) $ . | 3 |
308 | Find the projection of the vector $ \vec{v_1} = \left(13,~8\right) $ on the vector $ \vec{v_2} = \left(5,~-3\right) $. | 3 |
309 | Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(-8,~5\right) $ . | 3 |
310 | Find the angle between vectors $ \left(-2,~4\right)$ and $\left(8,~-16\right)$. | 3 |
311 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 10000 },~-\dfrac{ 7 }{ 5000 }\right) $ and $ \vec{v_2} = \left(-0.9082,~0.4186\right) $ . | 3 |
312 | Find the angle between vectors $ \left(4,~2\right)$ and $\left(4.4721,~2.2361\right)$. | 3 |
313 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(3,~24\right) $ . | 3 |
314 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(-10,~7\right) $ . | 3 |
315 | Find the angle between vectors $ \left(2,~2,~2\right)$ and $\left(1,~-1,~1\right)$. | 3 |
316 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-15,~5\right) $ . | 3 |
317 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 3 |
318 | Find the difference of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 3 |
319 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~60\right) $ . | 3 |
320 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~5\right) $ . | 3 |
321 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~5\right) $ . | 3 |
322 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ . | 3 |
323 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 3 |
324 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 5 }{ 13 },~\dfrac{ 12 }{ 13 }\right) $ . | 3 |
325 | Determine whether the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(-10,~7\right) $ are linearly independent or dependent. | 3 |
326 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ . | 3 |
327 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-1,~2\right) $ and $ \vec{v_2} = \left(4,~3,~-2\right) $ . | 3 |
328 | Find the angle between vectors $ \left(11.6881,~32.6073\right)$ and $\left(7.8137,~6.5564\right)$. | 3 |
329 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 3 |
330 | Find the angle between vectors $ \left(2,~10\right)$ and $\left(5,~-2\right)$. | 3 |
331 | Find the angle between vectors $ \left(9,~2\right)$ and $\left(3,~1\right)$. | 3 |
332 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(6,~-2\right) $ . | 3 |
333 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 231 }{ 10 },~-\dfrac{ 16 }{ 5 }\right) $ . | 3 |
334 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 3 |
335 | Determine whether the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(8,~2\right) $ are linearly independent or dependent. | 3 |
336 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(8,~26\right) $ . | 3 |
337 | Find the projection of the vector $ \vec{v_1} = \left(0,~1,~-3\right) $ on the vector $ \vec{v_2} = \left(-64,~-2,~30\right) $. | 3 |
338 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 3 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ . | 3 |
339 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~1\right) $ and $ \vec{v_2} = \left(1,~8\right) $ . | 3 |
340 | Find the difference of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 3 |
341 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(-2,~-5\right) $ . | 3 |
342 | Find the projection of the vector $ \vec{v_1} = \left(-3,~-6\right) $ on the vector $ \vec{v_2} = \left(-5,~2\right) $. | 3 |
343 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~-4\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ . | 3 |
344 | Find the angle between vectors $ \left(7,~5\right)$ and $\left(0,~8\right)$. | 3 |
345 | Find the projection of the vector $ \vec{v_1} = \left(-4,~6\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 3 |
346 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2\right) $ . | 3 |
347 | Find the difference of the vectors $ \vec{v_1} = \left(0,~10\right) $ and $ \vec{v_2} = \left(0,~10\right) $ . | 3 |
348 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 3 |
349 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(-3,~-3\right) $ . | 3 |
350 | Find the angle between vectors $ \left(1,~-3\right)$ and $\left(5,~\dfrac{ 1 }{ 2 }\right)$. | 3 |