Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
351 | Find the sum of the vectors $ \vec{v_1} = \left(-28,~4\right) $ and $ \vec{v_2} = \left(11,~15\right) $ . | 3 |
352 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 3 |
353 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 3 |
354 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~8\right) $ . | 3 |
355 | Determine whether the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ are linearly independent or dependent. | 3 |
356 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(2,~10\right) $ . | 3 |
357 | Find the angle between vectors $ \left(16,~12\right)$ and $\left(32,~25\right)$. | 3 |
358 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~5\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 3 |
359 | Find the projection of the vector $ \vec{v_1} = \left(-1,~1\right) $ on the vector $ \vec{v_2} = \left(3,~3\right) $. | 3 |
360 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-5\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 3 |
361 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(-3,~8\right) $ . | 3 |
362 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 3 |
363 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 3 |
364 | Find the angle between vectors $ \left(\dfrac{ 26 }{ 5 },~\dfrac{ 5 }{ 2 },~-\dfrac{ 9 }{ 2 }\right)$ and $\left(-3,~4,~-\dfrac{ 5 }{ 4 }\right)$. | 3 |
365 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 3 |
366 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~\sqrt{ 12 }\right) $ . | 3 |
367 | Find the difference of the vectors $ \vec{v_1} = \left(-7,~0\right) $ and $ \vec{v_2} = \left(8,~-1\right) $ . | 3 |
368 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-36,~-37\right) $ . | 3 |
369 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5.2,~2.5,~-4.5\right) $ and $ \vec{v_2} = \left(-3,~4,~-1.25\right) $ . | 3 |
370 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(0,~6\right) $ . | 3 |
371 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 3 |
372 | Find the angle between vectors $ \left(-2,~5,~-3\right)$ and $\left(4,~-6,~8\right)$. | 3 |
373 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{\sqrt{ 3 }}{ 2 },~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(- \dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right) $ . | 3 |
374 | Find the angle between vectors $ \left(50,~57\right)$ and $\left(29,~1\right)$. | 3 |
375 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(0,~-6\right) $ . | 3 |
376 | Find the projection of the vector $ \vec{v_1} = \left(1,~1\right) $ on the vector $ \vec{v_2} = \left(6,~3\right) $. | 3 |
377 | Determine whether the vectors $ \vec{v_1} = \left(3,~-2,~4\right) $, $ \vec{v_2} = \left(1,~-2,~3\right) $ and $ \vec{v_3} = \left(3,~2,~-1\right)$ are linearly independent or dependent. | 3 |
378 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 69503 }{ 100000 },~0.0652,~\dfrac{ 30519 }{ 3125 }\right) $ and $ \vec{v_2} = \left(0,~0,~\dfrac{ 49 }{ 5 }\right) $ . | 3 |
379 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1\right) $ . | 3 |
380 | Find the angle between vectors $ \left(5,~-2\right)$ and $\left(-4,~3\right)$. | 3 |
381 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 3 |
382 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-3,~0\right) $ . | 3 |
383 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-1\right) $ . | 3 |
384 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-4\right) $ . | 3 |
385 | Find the angle between vectors $ \left(25,~4\right)$ and $\left(35,~1\right)$. | 3 |
386 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~-49\right) $ and $ \vec{v_2} = \left(-48,~-72\right) $ . | 3 |
387 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 3 |
388 | Find the angle between vectors $ \left(25,~24\right)$ and $\left(47,~1\right)$. | 3 |
389 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-2\right) $ . | 3 |
390 | Calculate the dot product of the vectors $ \vec{v_1} = \left(32,~64\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 3 |
391 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-190,~321\right) $ . | 3 |
392 | Find the angle between vectors $ \left(\dfrac{ 69503 }{ 100000 },~0.0652,~\dfrac{ 30519 }{ 3125 }\right)$ and $\left(0,~0,~\dfrac{ 49 }{ 5 }\right)$. | 3 |
393 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 3 |
394 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(5,~0.5\right) $ . | 3 |
395 | Find the angle between vectors $ \left(5,~6\right)$ and $\left(4,~2\right)$. | 3 |
396 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ . | 3 |
397 | Find the angle between vectors $ \left(-1,~0\right)$ and $\left(0,~5\right)$. | 3 |
398 | Find the projection of the vector $ \vec{v_1} = \left(0,~1,~-3\right) $ on the vector $ \vec{v_2} = \left(2,~-1,~4\right) $. | 3 |
399 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-2\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 3 |
400 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 3 |