Vectors

(the database of solved problems)

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

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ID	Problem	Count
2001	Find the angle between vectors $(4, - 4)$ and $(- 12, - 12)$ .	2
2002	Find the angle between vectors $(4, - 4)$ and $(1, - 4)$ .	2
2003	Find the angle between vectors $(4, - 4)$ and $(- 1, - 3)$ .	2
2004	Calculate the dot product of the vectors $v_{1} = (33.3793, 536.4621)$ and $v_{2} = (44.7848, 528.8015)$ .	2
2005	Find the projection of the vector $v_{1} = (33.3793, 536.4621)$ on the vector $v_{2} = (44.7848, 528.8015)$ .	2
2006	Find the magnitude of the vector $∥ v ∥ = (- 1, 8)$ .	2
2007	Find the projection of the vector $v_{1} = (- 1, 4)$ on the vector $v_{2} = (\frac{7}{2}, - \frac{5}{4})$ .	2
2008	Find the magnitude of the vector $∥ v ∥ = (- 46, - 42)$ .	2
2009	Calculate the dot product of the vectors $v_{1} = (3, - 3, 5)$ and $v_{2} = (- 2, 4, - 1)$ .	2
2010	Find the angle between vectors $(- 3, - 7)$ and $(4, - 4)$ .	2
2011	Find the sum of the vectors $v_{1} = (1, 4)$ and $v_{2} = (3, - 1)$ .	2
2012	Calculate the dot product of the vectors $v_{1} = (1, 4)$ and $v_{2} = (3, - 1)$ .	2
2013	Calculate the dot product of the vectors $v_{1} = (- 1, 0)$ and $v_{2} = (0, 2)$ .	2
2014	Find the projection of the vector $v_{1} = (- 19, - 9, 16)$ on the vector $v_{2} = (- 6, - 2, 6)$ .	2
2015	Find the sum of the vectors $v_{1} = (\frac{14}{5}, - 1)$ and $v_{2} = (0, 2)$ .	2
2016	Find the sum of the vectors $v_{1} = (\frac{14}{5}, 1)$ and $v_{2} = (- \frac{17}{10}, - \frac{47}{10})$ .	2
2017	Find the sum of the vectors $v_{1} = (\frac{173}{10}, 10)$ and $v_{2} = (- \frac{63}{10}, \frac{68}{5})$ .	2
2018	Find the magnitude of the vector $∥ v ∥ = (3, 2)$ .	2
2019	Find the magnitude of the vector $∥ v ∥ = (\frac{173}{10}, 10)$ .	2
2020	Find the angle between vectors $(\frac{173}{10}, 10)$ and $(- \frac{63}{10}, \frac{68}{5})$ .	2
2021	Determine whether the vectors $v_{1} = (1, 2)$ and $v_{2} = (3, 4)$ are linearly independent or dependent.	2
2022	Find the magnitude of the vector $∥ v ∥ = (\frac{71}{1000}, \frac{833}{1000}, \frac{137}{200})$ .	2
2023	Find the sum of the vectors $v_{1} = (15, 14)$ and $v_{2} = (4, 11)$ .	2
2024	Find the projection of the vector $v_{1} = (15.898, 25.441)$ on the vector $v_{2} = (6.84, 18.79)$ .	2
2025	Find the difference of the vectors $v_{1} = (24, 10)$ and $v_{2} = (- 15, 20)$ .	2
2026	Find the projection of the vector $v_{1} = (3, - 2)$ on the vector $v_{2} = (5, 1)$ .	2
2027	Find the magnitude of the vector $∥ v ∥ = (- 1, 25)$ .	2
2028	Calculate the dot product of the vectors $v_{1} = (\frac{5}{13}, \frac{12}{13})$ and $v_{2} = (- 4, 8)$ .	2
2029	Find the angle between vectors $(\frac{5}{13}, \frac{12}{13})$ and $(- 4, 8)$ .	2
2030	Find the sum of the vectors $v_{1} = (4, 3)$ and $v_{2} = (2, 1)$ .	2
2031	Calculate the cross product of the vectors $v_{1} = (- 7, - 6, 9)$ and $v_{2} = (5, - 3, 4)$ .	2
2032	Calculate the dot product of the vectors $v_{1} = (- 1, 3)$ and $v_{2} = (1, 5)$ .	2
2033	Find the sum of the vectors $v_{1} = (0.2, 30)$ and $v_{2} = (0.2, 120)$ .	2
2034	Find the magnitude of the vector $∥ v ∥ = (2, 3)$ .	2
2035	Calculate the dot product of the vectors $v_{1} = (3, - 1, 2)$ and $v_{2} = (3, - 4, 2)$ .	2
2036	Find the sum of the vectors $v_{1} = (4, 0)$ and $v_{2} = (1, 2)$ .	2
2037	Find the sum of the vectors $v_{1} = (1, 2)$ and $v_{2} = (4, 0)$ .	2
2038	Find the sum of the vectors $v_{1} = (1, 2)$ and $v_{2} = (- 4, 2)$ .	2
2039	Find the sum of the vectors $v_{1} = (4, 0)$ and $v_{2} = (- 3, 4)$ .	2
2040	Find the sum of the vectors $v_{1} = (2, 2)$ and $v_{2} = (2, 2)$ .	2
2041	Find the difference of the vectors $v_{1} = (0, - 4)$ and $v_{2} = (2, - 5)$ .	2
2042	Find the sum of the vectors $v_{1} = (1, 4)$ and $v_{2} = (3, 2)$ .	2
2043	Find the magnitude of the vector $∥ v ∥ = (- 1, 5)$ .	2
2044	Find the angle between vectors $(\frac{26}{5}, - \frac{43}{10})$ and $(- \frac{71}{10}, - \frac{16}{5})$ .	2
2045	Calculate the dot product of the vectors $v_{1} = (\frac{25}{4}, - \frac{19}{5})$ and $v_{2} = (- \frac{23}{5}, \frac{11}{4})$ .	2
2046	Find the projection of the vector $v_{1} = (- 2, 6)$ on the vector $v_{2} = (- 9, - 3)$ .	2
2047	Find the magnitude of the vector $∥ v ∥ = (4, - 2)$ .	2
2048	Find the magnitude of the vector $∥ v ∥ = (\frac{43}{5}, - \frac{13}{2})$ .	2
2049	Find the angle between vectors $(3, 0)$ and $(2, 0)$ .	2
2050	Find the magnitude of the vector $∥ v ∥ = (5, 0)$ .	2