Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
401 | Find the angle between vectors $ \left(3,~-2\right)$ and $\left(5,~1\right)$. | 3 |
402 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~1\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 3 |
403 | Find the angle between vectors $ \left(4,~1\right)$ and $\left(-5,~-4\right)$. | 3 |
404 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~0\right) $ and $ \vec{v_2} = \left(5,~8\right) $ . | 3 |
405 | Find the angle between vectors $ \left(0,~4\right)$ and $\left(-5,~1\right)$. | 3 |
406 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-4\right) $ . | 3 |
407 | Find the difference of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 3 |
408 | Find the angle between vectors $ \left(1,~-4\right)$ and $\left(2,~0\right)$. | 3 |
409 | Find the angle between vectors $ \left(9,~8\right)$ and $\left(2,~0\right)$. | 3 |
410 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-3\right) $ . | 3 |
411 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 4 },~\dfrac{ 2 }{ 5 }\right) $ and $ \vec{v_2} = \left(-5,~-\dfrac{ 5 }{ 4 }\right) $ . | 3 |
412 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-4\right) $ and $ \vec{v_2} = \left(6,~-8\right) $ . | 3 |
413 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~2\right) $ . | 3 |
414 | Find the sum of the vectors $ \vec{v_1} = \left(-19.05,~11\right) $ and $ \vec{v_2} = \left(-5.73,~-32.5\right) $ . | 3 |
415 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 3 |
416 | Find the angle between vectors $ \left(110,~0\right)$ and $\left(110,~240\right)$. | 3 |
417 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 3 |
418 | Find the angle between vectors $ \left(4,~1\right)$ and $\left(1,~4\right)$. | 3 |
419 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 3 |
420 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 3 |
421 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(-3,~1\right)$. | 3 |
422 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~-1\right) $ . | 3 |
423 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~1,~2\right) $ . | 3 |
424 | Find the difference of the vectors $ \vec{v_1} = \left(-24,~21\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 3 |
425 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~10\right) $ . | 3 |
426 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ . | 3 |
427 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ . | 2 |
428 | Find the angle between vectors $ \left(\dfrac{ 62 }{ 5 },~45\right)$ and $\left(\dfrac{ 26 }{ 5 },~90\right)$. | 2 |
429 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
430 | Find the difference of the vectors $ \vec{v_1} = \left(30,~159\right) $ and $ \vec{v_2} = \left(\dfrac{ 27 }{ 2 },~\dfrac{ 85 }{ 2 }\right) $ . | 2 |
431 | Find the difference of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-4,~1\right) $ . | 2 |
432 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\sqrt{ 3 },~3\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 2 |
433 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~13\right) $ and $ \vec{v_2} = \left(-42,~-34\right) $ . | 2 |
434 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~6\right) $ . | 2 |
435 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~1\right) $ on the vector $ \vec{v_2} = \left(0,~2,~1\right) $. | 2 |
436 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(9,~12\right) $ . | 2 |
437 | Find the projection of the vector $ \vec{v_1} = \left(5,~2,~5\right) $ on the vector $ \vec{v_2} = \left(2,~-1,~2\right) $. | 2 |
438 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ . | 2 |
439 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~2\right) $ . | 2 |
440 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 151 }{ 100 },~\dfrac{ 281 }{ 100 }\right) $ . | 2 |
441 | Find the sum of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 2 |
442 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~8\right) $ and $ \vec{v_2} = \left(5,~4\right) $ . | 2 |
443 | Find the projection of the vector $ \vec{v_1} = \left(4,~0\right) $ on the vector $ \vec{v_2} = \left(5,~-2\right) $. | 2 |
444 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~-2\right) $ . | 2 |
445 | Find the angle between vectors $ \left(30,~0\right)$ and $\left(47,~0\right)$. | 2 |
446 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ . | 2 |
447 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(4,~5,~6\right) $ . | 2 |
448 | Find the angle between vectors $ \left(3,~3,~10\right)$ and $\left(7,~5,~0\right)$. | 2 |
449 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 72 }{ 41 },~-\dfrac{ 320 }{ 41 }\right) $ . | 2 |
450 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~5\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ . | 2 |