Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3151 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~3,~3\right) $ and $ \vec{v_2} = \left(2,~4,~-5\right) $ . | 1 |
| 3152 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3,~3\right) $ and $ \vec{v_2} = \left(2,~4,~-5\right) $ . | 1 |
| 3153 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 23 }{ 20 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 41 }{ 20 },~0\right) $ . | 1 |
| 3154 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ . | 1 |
| 3155 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 1 |
| 3156 | Find the sum of the vectors $ \vec{v_1} = \left(18,~-3\right) $ and $ \vec{v_2} = \left(-15,~20\right) $ . | 1 |
| 3157 | Find the angle between vectors $ \left(-1,~0,~0\right)$ and $\left(1,~1,~1\right)$. | 1 |
| 3158 | Find the angle between vectors $ \left(-1,~0,~0\right)$ and $\left(2,~0,~-2\right)$. | 1 |
| 3159 | Find the angle between vectors $ \left(0,~1,~1\right)$ and $\left(1,~-1,~-3\right)$. | 1 |
| 3160 | Determine whether the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(-6,~10\right) $ are linearly independent or dependent. | 1 |
| 3161 | Find the angle between vectors $ \left(0,~5\right)$ and $\left(4,~0\right)$. | 1 |
| 3162 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~5\right) $ . | 1 |
| 3163 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2\right) $ . | 1 |
| 3164 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~0,~3\right) $ . | 1 |
| 3165 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-5\right) $ . | 1 |
| 3166 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(-7,~24\right)$. | 1 |
| 3167 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(6,~2\right) $ . | 1 |
| 3168 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~0\right) $ . | 1 |
| 3169 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~1\right) $ . | 1 |
| 3170 | Find the angle between vectors $ \left(-3,~1\right)$ and $\left(3,~9\right)$. | 1 |
| 3171 | Find the sum of the vectors $ \vec{v_1} = \left(8,~6\right) $ and $ \vec{v_2} = \left(-7,~-5\right) $ . | 1 |
| 3172 | Find the difference of the vectors $ \vec{v_1} = \left(-7,~-5\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 1 |
| 3173 | Find the sum of the vectors $ \vec{v_1} = \left(12,~-4\right) $ and $ \vec{v_2} = \left(32,~24\right) $ . | 1 |
| 3174 | Find the sum of the vectors $ \vec{v_1} = \left(14,~10\right) $ and $ \vec{v_2} = \left(24,~18\right) $ . | 1 |
| 3175 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~6\right) $ and $ \vec{v_2} = \left(6,~4\right) $ . | 1 |
| 3176 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-1,~1\right) $ and $ \vec{v_2} = \left(1,~2,~3\right) $ . | 1 |
| 3177 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ . | 1 |
| 3178 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-5\right) $ and $ \vec{v_2} = \left(10,~-2\right) $ . | 1 |
| 3179 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(8,~-6\right) $ . | 1 |
| 3180 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~2\right) $ and $ \vec{v_2} = \left(2,~-10\right) $ . | 1 |
| 3181 | Find the angle between vectors $ \left(3,~-5\right)$ and $\left(6,~-4\right)$. | 1 |
| 3182 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(-4,~-6\right)$. | 1 |
| 3183 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~3\right) $ . | 1 |
| 3184 | Find the difference of the vectors $ \vec{v_1} = \left(0,~2\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 1 |
| 3185 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1,~0\right) $, $ \vec{v_2} = \left(2,~0,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 3186 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1,~0\right) $, $ \vec{v_2} = \left(0,~0,~2\right) $ and $ \vec{v_3} = \left(2,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 3187 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1\right) $ . | 1 |
| 3188 | Find the projection of the vector $ \vec{v_1} = \left(3,~2\right) $ on the vector $ \vec{v_2} = \left(1,~3\right) $. | 1 |
| 3189 | Find the angle between vectors $ \left(5,~-2,~4\right)$ and $\left(8,~3,~-2\right)$. | 1 |
| 3190 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~7\right) $ . | 1 |
| 3191 | Find the sum of the vectors $ \vec{v_1} = \left(-12,~-6\right) $ and $ \vec{v_2} = \left(30,~-20\right) $ . | 1 |
| 3192 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~4\right) $ . | 1 |
| 3193 | Find the magnitude of the vector $ \| \vec{v} \| = \left(28,~50\right) $ . | 1 |
| 3194 | Determine whether the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(-8,~1\right) $ are linearly independent or dependent. | 1 |
| 3195 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~-3\right) $ . | 1 |
| 3196 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 3 }{ 2 },~1,~1\right) $ . | 1 |
| 3197 | Determine whether the vectors $ \vec{v_1} = \left(-6,~4\right) $ and $ \vec{v_2} = \left(3,~3\right) $ are linearly independent or dependent. | 1 |
| 3198 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~4\right) $ and $ \vec{v_2} = \left(3,~3\right) $ . | 1 |
| 3199 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-3\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 1 |
| 3200 | Find the projection of the vector $ \vec{v_1} = \left(-1,~3\right) $ on the vector $ \vec{v_2} = \left(4,~3\right) $. | 1 |
