Vectors – Solved Problems Database

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

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ID	Problem	Count
501	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~11,~10\right) $ .	2
502	Find the sum of the vectors $ \vec{v_1} = \left(-2,~58\right) $ and $ \vec{v_2} = \left(3,~17\right) $ .	2
503	Find the difference of the vectors $ \vec{v_1} = \left(10,~10\right) $ and $ \vec{v_2} = \left(21,~21\right) $ .	2
504	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-1\right) $ .	2
505	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~-12\right) $ .	2
506	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~-8,~-4\right) $ .	2
507	Find the sum of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(4,~1\right) $ .	2
508	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 16 }{ 5 },~\dfrac{ 24 }{ 5 }\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ .	2
509	Find the difference of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(4,~1\right) $ .	2
510	Find the angle between vectors $ \left(0,~4\right)$ and $\left(4,~1\right)$.	2
511	Find the difference of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ .	2
512	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(7,~5\right) $ .	2
513	Find the angle between vectors $ \left(0,~40\right)$ and $\left(18,~0\right)$.	2
514	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~0,~7\right) $ .	2
515	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~2\right) $ .	2
516	Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~4,~16\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ .	2
517	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
518	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~-4\right) $ .	2
519	Find the sum of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-16,~-20\right) $ .	2
520	Find the sum of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-20,~-25\right) $ .	2
521	Determine whether the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-6,~10\right) $ are linearly independent or dependent.	2
522	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-10,~10\right) $ .	2
523	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~22\right) $ .	2
524	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(15,~-15\right) $ .	2
525	Find the sum of the vectors $ \vec{v_1} = \left(-9,~4\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ .	2
526	Determine whether the vectors $ \vec{v_1} = \left(0,~-32\right) $ and $ \vec{v_2} = \left(6,~-185\right) $ are linearly independent or dependent.	2
527	Find the angle between vectors $ \left(0,~-32\right)$ and $\left(6,~-185\right)$.	2
528	Find the sum of the vectors $ \vec{v_1} = \left(0,~-32\right) $ and $ \vec{v_2} = \left(6,~-185\right) $ .	2
529	Find the difference of the vectors $ \vec{v_1} = \left(7,~9\right) $ and $ \vec{v_2} = \left(-30,~40\right) $ .	2
530	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-6\right) $ .	2
531	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~-4\right) $ .	2
532	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~3,~1\right) $ .	2
533	Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 23 }{ 20 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 41 }{ 20 },~0\right) $ .	2
534	Find the difference of the vectors $ \vec{v_1} = \left(-4,~6\right) $ and $ \vec{v_2} = \left(2,~1\right) $ .	2
535	Find the difference of the vectors $ \vec{v_1} = \left(-4,~6\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ .	2
536	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(10,~-3\right) $ .	2
537	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(10,~-8\right) $ .	2
538	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-4\right) $ and $ \vec{v_2} = \left(7,~1\right) $ .	2
539	Find the difference of the vectors $ \vec{v_1} = \left(5,~7\right) $ and $ \vec{v_2} = \left(-9,~28\right) $ .	2
540	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ .	2
541	Find the sum of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 143 }{ 10 },~-\dfrac{ 117 }{ 50 }\right) $ .	2
542	Find the sum of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(16,~12\right) $ .	2
543	Find the sum of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ .	2
544	Find the difference of the vectors $ \vec{v_1} = \left(12,~-4\right) $ and $ \vec{v_2} = \left(32,~24\right) $ .	2
545	Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-4\right) $ and $ \vec{v_2} = \left(1,~-9\right) $ .	2
546	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~6\right) $ .	2
547	Find the sum of the vectors $ \vec{v_1} = \left(24,~-24\right) $ and $ \vec{v_2} = \left(-7,~10\right) $ .	2
548	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~-1\right) $ .	2
549	Find the difference of the vectors $ \vec{v_1} = \left(-4,~-1\right) $ and $ \vec{v_2} = \left(4,~2\right) $ .	2
550	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~-1\right) $ .	2