Vectors – Solved Problems Database

All the problems and solutions shown below were generated using the Vectors Calculator.

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ID	Problem	Count
451	Find the projection of the vector $ \vec{v_1} = \left(2,~1\right) $ on the vector $ \vec{v_2} = \left(-3,~4\right) $.	2
452	Find the angle between vectors $ \left(3,~0\right)$ and $\left(5,~5\right)$.	2
453	Find the angle between vectors $ \left(5,~6\right)$ and $\left(-1,~4\right)$.	2
454	Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~6,~2\right) $ and $ \vec{v_2} = \left(2,~3,~2\right) $ .	2
455	Find the angle between vectors $ \left(-3,~5\right)$ and $\left(-7,~-1\right)$.	2
456	Find the angle between vectors $ \left(-3,~5\right)$ and $\left(-4,~-6\right)$.	2
457	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-8,~6\right) $ .	2
458	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ .	2
459	Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(10,~10\right) $ .	2
460	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~1\right) $ .	2
461	Find the angle between vectors $ \left(5,~1,~0\right)$ and $\left(-16,~-12,~-8\right)$.	2
462	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ .	2
463	Find the difference of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(4,~1\right) $ .	2
464	Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(-3,~-8\right) $ .	2
465	Find the angle between vectors $ \left(5,~-1\right)$ and $\left(4,~6\right)$.	2
466	Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~5\right) $ and $ \vec{v_2} = \left(-2,~-1,~4\right) $ .	2
467	Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ .	2
468	Find the angle between vectors $ \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right)$ and $\left(0,~1,~0\right)$.	2
469	Find the difference of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ .	2
470	Find the projection of the vector $ \vec{v_1} = \left(0,~1,~0\right) $ on the vector $ \vec{v_2} = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $.	2
471	Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ .	2
472	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 6879 }{ 5000 },~-0.192,~-1\right) $ .	2
473	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~42\right) $ .	2
474	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-9,~40\right) $ .	2
475	Find the angle between vectors $ \left(-1,~5,~6\right)$ and $\left(2,~3,~-1\right)$.	2
476	Find the angle between vectors $ \left(80,~0\right)$ and $\left(170,~0\right)$.	2
477	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ .	2
478	Find the difference of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(3,~10\right) $ .	2
479	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 151 }{ 100 },~\dfrac{ 281 }{ 100 }\right) $ .	2
480	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~5\right) $ .	2
481	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-30,~23\right) $ .	2
482	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-7,~-24\right) $ .	2
483	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-8,~6\right) $ .	2
484	Find the angle between vectors $ \left(12,~11,~5\right)$ and $\left(4,~15,~5\right)$.	2
485	Find the sum of the vectors $ \vec{v_1} = \left(8,~6\right) $ and $ \vec{v_2} = \left(-8,~5\right) $ .	2
486	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-9,~-19\right) $ .	2
487	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~6\right) $ .	2
488	Find the difference of the vectors $ \vec{v_1} = \left(4,~-2\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ .	2
489	Find the angle between vectors $ \left(3,~-5\right)$ and $\left(6,~-10\right)$.	2
490	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-5,~-4\right) $ .	2
491	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~4\right) $ .	2
492	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~4\right) $ .	2
493	Find the difference of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-7,~8\right) $ .	2
494	Find the sum of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-7,~8\right) $ .	2
495	Find the difference of the vectors $ \vec{v_1} = \left(-5,~12\right) $ and $ \vec{v_2} = \left(9,~-1\right) $ .	2
496	Determine whether the vectors $ \vec{v_1} = \left(-5,~12\right) $ and $ \vec{v_2} = \left(9,~-1\right) $ are linearly independent or dependent.	2
497	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-5,~12\right) $ .	2
498	Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~12\right) $ and $ \vec{v_2} = \left(9,~-1\right) $ .	2
499	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-1,~0\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ .	2
500	Find the angle between vectors $ \left(12,~35\right)$ and $\left(60,~-11\right)$.	2