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
1001	Find the projection of the vector $v_{1} = (3, 4)$ on the vector $v_{2} = (6, 8)$ .	2
1002	Find the difference of the vectors $v_{1} = (3, 4)$ and $v_{2} = (3, 4)$ .	2
1003	Find the sum of the vectors $v_{1} = (6, - 2)$ and $v_{2} = (0, - 8)$ .	2
1004	Find the angle between vectors $(0, 4)$ and $(\frac{3 2}{2}, \frac{3 2}{2})$ .	2
1005	Find the difference of the vectors $v_{1} = (3, - 8)$ and $v_{2} = (7, \frac{21}{8})$ .	2
1006	Find the sum of the vectors $v_{1} = (7, - 4)$ and $v_{2} = (- 8, 9)$ .	2
1007	Find the difference of the vectors $v_{1} = (- 27, 24)$ and $v_{2} = (5, - 40)$ .	2
1008	Find the difference of the vectors $v_{1} = (- 27, 24)$ and $v_{2} = (- 5, - 40)$ .	2
1009	Find the magnitude of the vector $∥ v ∥ = (- 7, - 4)$ .	2
1010	Find the magnitude of the vector $∥ v ∥ = (7, - 24)$ .	2
1011	Find the difference of the vectors $v_{1} = (28, - 1)$ and $v_{2} = (- 9, 0)$ .	2
1012	Find the difference of the vectors $v_{1} = (- 20, 45)$ and $v_{2} = (37, - 1)$ .	2
1013	Find the difference of the vectors $v_{1} = (- 20, 45)$ and $v_{2} = (- 37, 1)$ .	2
1014	Find the difference of the vectors $v_{1} = (6, 0)$ and $v_{2} = (3, 33)$ .	2
1015	Find the projection of the vector $v_{1} = (6, 0)$ on the vector $v_{2} = (3, 33)$ .	2
1016	Find the magnitude of the vector $∥ v ∥ = (2, - 2, 1)$ .	2
1017	Find the magnitude of the vector $∥ v ∥ = (\frac{26}{5}, \frac{5}{2}, - \frac{9}{2})$ .	2
1018	Find the magnitude of the vector $∥ v ∥ = (40, - 30)$ .	2
1019	Find the sum of the vectors $v_{1} = (3, 4)$ and $v_{2} = (5, 7)$ .	2
1020	Find the magnitude of the vector $∥ v ∥ = (0, 0)$ .	2
1021	Find the difference of the vectors $v_{1} = (6, 9, 3)$ and $v_{2} = (1, 3, 0)$ .	2
1022	Find the sum of the vectors $v_{1} = (- 2, 9)$ and $v_{2} = (5, 6)$ .	2
1023	Find the difference of the vectors $v_{1} = (- 6, 7)$ and $v_{2} = (3, 8)$ .	2
1024	Find the magnitude of the vector $∥ v ∥ = (2, - 5)$ .	2
1025	Find the sum of the vectors $v_{1} = (- 4, - 4)$ and $v_{2} = (1, - 4)$ .	2
1026	Find the difference of the vectors $v_{1} = (- 4, - 4)$ and $v_{2} = (1, - 4)$ .	2
1027	Calculate the dot product of the vectors $v_{1} = (- 9, 7)$ and $v_{2} = (10, 4)$ .	2
1028	Find the magnitude of the vector $∥ v ∥ = (- 9, 7)$ .	2
1029	Find the magnitude of the vector $∥ v ∥ = (110, 0)$ .	2
1030	Find the projection of the vector $v_{1} = (1, 2)$ on the vector $v_{2} = (\frac{1}{10}, \frac{1}{5})$ .	2
1031	Find the magnitude of the vector $∥ v ∥ = (- \frac{81}{1000}, - \frac{327}{500})$ .	2
1032	Find the magnitude of the vector $∥ v ∥ = (1, 1)$ .	2
1033	Find the sum of the vectors $v_{1} = (6, 0)$ and $v_{2} = (1, 1)$ .	2
1034	Calculate the cross product of the vectors $v_{1} = (1, 0, 3)$ and $v_{2} = (0, 3, 1)$ .	2
1035	Calculate the dot product of the vectors $v_{1} = (2, 2)$ and $v_{2} = (3, - 6)$ .	2
1036	Find the magnitude of the vector $∥ v ∥ = (- 6, 8)$ .	2
1037	Find the magnitude of the vector $∥ v ∥ = (32, - 24)$ .	2
1038	Find the angle between vectors $(3, 4)$ and $(- 8, 7)$ .	2
1039	Calculate the dot product of the vectors $v_{1} = (1275, 2500)$ and $v_{2} = (\frac{66}{5}, \frac{41}{5})$ .	2
1040	Find the magnitude of the vector $∥ v ∥ = (0, 0)$ .	2
1041	Calculate the dot product of the vectors $v_{1} = (3, 4)$ and $v_{2} = (2, 8)$ .	2
1042	Find the angle between vectors $(3, 4)$ and $(2, 8)$ .	2
1043	Find the projection of the vector $v_{1} = (3, 4)$ on the vector $v_{2} = (2, 8)$ .	2
1044	Find the sum of the vectors $v_{1} = (- 1, 4)$ and $v_{2} = (3, - 2)$ .	2
1045	Calculate the dot product of the vectors $v_{1} = (4, - 24)$ and $v_{2} = (6, 1)$ .	2
1046	Find the angle between vectors $(- 2, 1)$ and $(- 1, - 4)$ .	2
1047	Find the magnitude of the vector $∥ v ∥ = (4, 5)$ .	2
1048	Determine whether the vectors $v_{1} = (4, 5)$ and $v_{2} = (- 5, 11)$ are linearly independent or dependent.	2
1049	Calculate the dot product of the vectors $v_{1} = (- 5, - 4)$ and $v_{2} = (- 2, \frac{1}{4})$ .	2
1050	Determine whether the vectors $v_{1} = (- 5, - 4)$ and $v_{2} = (- 2, \frac{1}{4})$ are linearly independent or dependent.	2