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
101	Calculate the dot product of the vectors $v_{1} = (5, 8)$ and $v_{2} = (- 9, 2)$ .	4
102	Find the magnitude of the vector $∥ v ∥ = (3, 2)$ .	4
103	Find the projection of the vector $v_{1} = (0, 3)$ on the vector $v_{2} = (6, 3)$ .	4
104	Find the magnitude of the vector $∥ v ∥ = (7, 7)$ .	4
105	Find the sum of the vectors $v_{1} = (3, 4)$ and $v_{2} = (- 7, 2)$ .	4
106	Find the magnitude of the vector $∥ v ∥ = (6, - 1)$ .	4
107	Calculate the dot product of the vectors $v_{1} = (6, - 2)$ and $v_{2} = (6, - 2)$ .	4
108	Find the projection of the vector $v_{1} = (- 10, - 7)$ on the vector $v_{2} = (- 8, 4)$ .	4
109	Calculate the cross product of the vectors $v_{1} = (1, 2, 3)$ and $v_{2} = (- 3, - 1, 2)$ .	4
110	Find the difference of the vectors $v_{1} = (0, - 16)$ and $v_{2} = (8, - 20)$ .	4
111	Find the projection of the vector $v_{1} = (8, 5)$ on the vector $v_{2} = (- 9, - 2)$ .	4
112	Calculate the dot product of the vectors $v_{1} = (6, - 1)$ and $v_{2} = (5, 7)$ .	4
113	Calculate the dot product of the vectors $v_{1} = (1, 1)$ and $v_{2} = (1, 1)$ .	4
114	Calculate the dot product of the vectors $v_{1} = (- 3, 0)$ and $v_{2} = (2, 0)$ .	4
115	Find the projection of the vector $v_{1} = (3, - 5)$ on the vector $v_{2} = (0, 1)$ .	4
116	Calculate the dot product of the vectors $v_{1} = (- 10, 2)$ and $v_{2} = (1, 5)$ .	4
117	Find the difference of the vectors $v_{1} = (- 2, 4)$ and $v_{2} = (- 3, - 3)$ .	4
118	Find the sum of the vectors $v_{1} = (2, - 5)$ and $v_{2} = (1, 4)$ .	4
119	Find the magnitude of the vector $∥ v ∥ = (9, 7)$ .	4
120	Find the magnitude of the vector $∥ v ∥ = (1, - 3)$ .	4
121	Find the angle between vectors $(- 7, - 5)$ and $(2, - 8)$ .	4
122	Find the magnitude of the vector $∥ v ∥ = (- 1, 4)$ .	4
123	Calculate the dot product of the vectors $v_{1} = (3, 4)$ and $v_{2} = (0, 0)$ .	4
124	Find the angle between vectors $(1, 3)$ and $(2, - 5)$ .	4
125	Find the difference of the vectors $v_{1} = (- 24, 21)$ and $v_{2} = (- 2, 1)$ .	4
126	Find the angle between vectors $(2, 1, - 4)$ and $(3, - 5, 2)$ .	4
127	Find the angle between vectors $(2, 1, - 4)$ and $(3, - 5, 2)$ .	4
128	Find the angle between vectors $(3, 4)$ and $(10, 4)$ .	4
129		4
130	Find the projection of the vector $v_{1} = (- 5, 8)$ on the vector $v_{2} = (- 6, - 7)$ .	4
131	Find the magnitude of the vector $∥ v ∥ = (9, - 7)$ .	4
132	Calculate the dot product of the vectors $v_{1} = (11, 1)$ and $v_{2} = (1, 11)$ .	4
133	Find the magnitude of the vector $∥ v ∥ = (- 8, - 7)$ .	4
134	Find the difference of the vectors $v_{1} = (3, 4)$ and $v_{2} = (- 1, 1)$ .	4
135	Find the magnitude of the vector $∥ v ∥ = (6, - 5)$ .	4
136	Find the magnitude of the vector $∥ v ∥ = (6, 2)$ .	4
137	Find the magnitude of the vector $∥ v ∥ = (- 3, 6)$ .	4
138	Determine whether the vectors $v_{1} = (1, 2)$ and $v_{2} = (2, 5)$ are linearly independent or dependent.	4
139	Find the magnitude of the vector $∥ v ∥ = (2, 4)$ .	4
140	Find the magnitude of the vector $∥ v ∥ = (- 4, - 5)$ .	4
141	Find the angle between vectors $(\frac{2}{5}, \frac{3}{10})$ and $(- \frac{3}{20}, \frac{1}{5})$ .	4
142	Find the angle between vectors $(2, 1, - 4)$ and $(3, - 5, 2)$ .	4
143	Find the magnitude of the vector $∥ v ∥ = (24, - 7)$ .	4
144	Find the difference of the vectors $v_{1} = (3, - 1)$ and $v_{2} = (- 4, - 2)$ .	4
145	Find the sum of the vectors $v_{1} = (4, 2)$ and $v_{2} = (- 8, - 2)$ .	4
146	Find the difference of the vectors $v_{1} = (2, 1)$ and $v_{2} = (1, 3)$ .	4
147	Find the sum of the vectors $v_{1} = (- 5, - 3)$ and $v_{2} = (3, - 8)$ .	4
148	Find the magnitude of the vector $∥ v ∥ = (1, 1)$ .	4
149	Find the magnitude of the vector $∥ v ∥ = (- 1, 2)$ .	4
150	Find the sum of the vectors $v_{1} = (0, 1)$ and $v_{2} = (0, 1)$ .	4