Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
151 | Find the angle between vectors $ \left(-2,~2\right)$ and $\left(0,~-4\right)$. | 4 |
152 | | 4 |
153 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 161 }{ 10 },~\dfrac{ 96 }{ 5 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 137 }{ 10 },~\dfrac{ 188 }{ 5 }\right) $ . | 4 |
154 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 4 |
155 | Find the projection of the vector $ \vec{v_1} = \left(-5,~8\right) $ on the vector $ \vec{v_2} = \left(-6,~-7\right) $. | 4 |
156 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 4 |
157 | Find the projection of the vector $ \vec{v_1} = \left(0,~3\right) $ on the vector $ \vec{v_2} = \left(6,~3\right) $. | 4 |
158 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0,~-1\right) $ . | 4 |
159 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-5\right) $ . | 4 |
160 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~5\right) $ are linearly independent or dependent. | 4 |
161 | Find the angle between vectors $ \left(1,~3\right)$ and $\left(2,~-5\right)$. | 4 |
162 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-10,~2\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 4 |
163 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~6\right) $ . | 4 |
164 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 4 |
165 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-7,~2\right) $ . | 4 |
166 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~6\right) $ . | 4 |
167 | Find the difference of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 4 |
168 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~-7\right) $ . | 4 |
169 | Find the angle between vectors $ \left(-7,~-5\right)$ and $\left(2,~-8\right)$. | 4 |
170 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-2\right) $ . | 4 |
171 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-5\right) $ . | 4 |
172 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(-5,~7\right) $ . | 4 |
173 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 4 |
174 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-3,~-3\right) $ . | 4 |
175 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(9,~9\right) $ . | 3 |
176 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 3 |
177 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~3\right) $ and $ \vec{v_2} = \left(-1,~2,~-4\right) $ . | 3 |
178 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3\right) $ . | 3 |
179 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~14\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 3 |
180 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~-18\right) $ and $ \vec{v_2} = \left(-7,~8\right) $ . | 3 |
181 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(0,~2\right) $ . | 3 |
182 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 49 }{ 100 },~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 27 }{ 500 },~-\dfrac{ 12 }{ 25 }\right) $ . | 3 |
183 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 3 |
184 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~4 \sqrt{ 3 }\right) $ . | 3 |
185 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-\sqrt{ 3 },~\dfrac{ 3 }{ 2 }\right) $ . | 3 |
186 | Find the sum of the vectors $ \vec{v_1} = \left(12,~9\right) $ and $ \vec{v_2} = \left(-6,~\dfrac{ 1039 }{ 100 }\right) $ . | 3 |
187 | Find the angle between vectors $ \left(3,~7\right)$ and $\left(-4,~-1\right)$. | 3 |
188 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-6\right) $ and $ \vec{v_2} = \left(-15,~8\right) $ . | 3 |
189 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1\right) $ . | 3 |
190 | Find the angle between vectors $ \left(5 \sqrt{ 2 },~-3\right)$ and $\left(17,~-26\right)$. | 3 |
191 | Find the sum of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 3 |
192 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-3\right) $ . | 3 |
193 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~7,~-9\right) $ and $ \vec{v_2} = \left(-11,~9,~-2\right) $ . | 3 |
194 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-4,~-12\right) $ . | 3 |
195 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-1,~2\right) $ . | 3 |
196 | Find the angle between vectors $ \left(9,~2\right)$ and $\left(-8,~-12\right)$. | 3 |
197 | Find the projection of the vector $ \vec{v_1} = \left(3020,~2800\right) $ on the vector $ \vec{v_2} = \left(1,~-1\right) $. | 3 |
198 | Find the angle between vectors $ \left(9,~2\right)$ and $\left(12,~-8\right)$. | 3 |
199 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1\right) $ . | 3 |
200 | Find the projection of the vector $ \vec{v_1} = \left(5,~-5,~2\right) $ on the vector $ \vec{v_2} = \left(1,~1,~5\right) $. | 3 |