Vectors

(the database of solved problems)

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

Select category

ID	Problem	Count
51	Find the projection of the vector $v_{1} = (2, - 6)$ on the vector $v_{2} = (- \frac{1}{3}, \frac{3}{5})$ .	5
52	Find the difference of the vectors $v_{1} = (9, 5)$ and $v_{2} = (1, 4)$ .	5
53	Find the sum of the vectors $v_{1} = (2, - 1)$ and $v_{2} = (- 1, 3)$ .	5
54	Find the difference of the vectors $v_{1} = (4, 2)$ and $v_{2} = (- 8, - 2)$ .	5
55	Find the magnitude of the vector $∥ v ∥ = (- 15, - 45)$ .	5
56	Find the magnitude of the vector $∥ v ∥ = (- 5, - 12)$ .	5
57	Find the magnitude of the vector $∥ v ∥ = (\frac{21}{10}, - \frac{16}{5})$ .	5
58	Find the magnitude of the vector $∥ v ∥ = (- 5, - 2)$ .	5
59	Find the magnitude of the vector $∥ v ∥ = (0, 2)$ .	5
60	Find the magnitude of the vector $∥ v ∥ = (- 1, 2)$ .	5
61	Calculate the dot product of the vectors $v_{1} = (5, - 9)$ and $v_{2} = (- 1, - 4)$ .	5
62	Find the magnitude of the vector $∥ v ∥ = (- 2, 3)$ .	5
63	Find the projection of the vector $v_{1} = (1, 2)$ on the vector $v_{2} = (10, 5)$ .	5
64	Find the magnitude of the vector $∥ v ∥ = (- 5, 9)$ .	5
65	Find the magnitude of the vector $∥ v ∥ = (- 1, 3)$ .	5
66	Calculate the dot product of the vectors $v_{1} = (1, 2, 3)$ and $v_{2} = (4, 5, 6)$ .	5
67	Find the difference of the vectors $v_{1} = (\frac{3}{4}, 2)$ and $v_{2} = (3, - 2)$ .	5
68	Find the angle between vectors $(5, - 3)$ and $(- 8, 8)$ .	5
69	Find the magnitude of the vector $∥ v ∥ = (1, 2, 3)$ .	5
70	Find the magnitude of the vector $∥ v ∥ = (- 5, 12)$ .	5
71	Calculate the dot product of the vectors $v_{1} = (4, 1)$ and $v_{2} = (1, 4)$ .	5
72	Find the angle between vectors $(4, 3)$ and $(2, 3)$ .	5
73	Find the sum of the vectors $v_{1} = (- \frac{2}{5}, \frac{3}{5})$ and $v_{2} = (5, 29)$ .	5
74	Find the magnitude of the vector $∥ v ∥ = (5, - 3)$ .	5
75	Find the sum of the vectors $v_{1} = (1, 1)$ and $v_{2} = (3, 4)$ .	5
76	Find the angle between vectors $(1, - 1)$ and $(1, - 1)$ .	5
77	Find the sum of the vectors $v_{1} = (1, 0)$ and $v_{2} = (1, 0)$ .	5
78	Find the difference of the vectors $v_{1} = (7, 1)$ and $v_{2} = (5, 5)$ .	5
79	Find the difference of the vectors $v_{1} = (10, - 1)$ and $v_{2} = (10, - 4)$ .	5
80	Find the angle between vectors $(- 78, 44)$ and $(87, 80)$ .	5
81	Find the sum of the vectors $v_{1} = (1, 0)$ and $v_{2} = (0, 1)$ .	5
82	Find the magnitude of the vector $∥ v ∥ = (5, 3)$ .	5
83	Calculate the dot product of the vectors $v_{1} = (- 4, 7)$ and $v_{2} = (28, - 49)$ .	5
84	Find the difference of the vectors $v_{1} = (- 4, - 1)$ and $v_{2} = (1, 5)$ .	5
85	Find the magnitude of the vector $∥ v ∥ = (3, 4)$ .	4
86	Calculate the dot product of the vectors $v_{1} = (6, - 1)$ and $v_{2} = (5, 7)$ .	4
87	Calculate the dot product of the vectors $v_{1} = (- 10, 2)$ and $v_{2} = (1, 5)$ .	4
88	Find the angle between vectors $(- 7, - 5)$ and $(2, - 8)$ .	4
89	Find the difference of the vectors $v_{1} = (- 2, 4)$ and $v_{2} = (- 3, - 3)$ .	4
90	Find the magnitude of the vector $∥ v ∥ = (- 1, 2)$ .	4
91	Find the sum of the vectors $v_{1} = (0, 1)$ and $v_{2} = (0, 1)$ .	4
92	Find the difference of the vectors $v_{1} = (- 5, 3)$ and $v_{2} = (- 3, 6)$ .	4
93	Find the sum of the vectors $v_{1} = (- 5, - 3)$ and $v_{2} = (3, - 8)$ .	4
94	Calculate the dot product of the vectors $v_{1} = (1, 1)$ and $v_{2} = (1, 1)$ .	4
95	Find the projection of the vector $v_{1} = (8, 5)$ on the vector $v_{2} = (- 9, - 2)$ .	4
96	Calculate the dot product of the vectors $v_{1} = (3, 2)$ and $v_{2} = (4, 2)$ .	4
97	Find the sum of the vectors $v_{1} = (4, 2)$ and $v_{2} = (- 8, - 2)$ .	4
98	Find the difference of the vectors $v_{1} = (3, - 1)$ and $v_{2} = (- 4, - 2)$ .	4
99	Calculate the dot product of the vectors $v_{1} = (1, 1)$ and $v_{2} = (2, 2)$ .	4
100	Find the sum of the vectors $v_{1} = (11, 2)$ and $v_{2} = (1, 4)$ .	4