Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3101 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3102 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-1,~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(-2,~3,~-2\right) $ . | 1 |
| 3103 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-1,~\dfrac{ 1 }{ 2 }\right) $ . | 1 |
| 3104 | Find the angle between vectors $ \left(4,~-1,~\dfrac{ 1 }{ 2 }\right)$ and $\left(-2,~3,~-2\right)$. | 1 |
| 3105 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-14,~-6\right) $ and $ \vec{v_2} = \left(15,~-3\right) $ . | 1 |
| 3106 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1,~0\right) $ and $ \vec{v_2} = \left(-2,~3,~-2\right) $ . | 1 |
| 3107 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 16 }{ 5 },~\dfrac{ 24 }{ 5 }\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ are linearly independent or dependent. | 1 |
| 3108 | Find the projection of the vector $ \vec{v_1} = \left(0,~4\right) $ on the vector $ \vec{v_2} = \left(4,~1\right) $. | 1 |
| 3109 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~7\right) $ . | 1 |
| 3110 | Find the sum of the vectors $ \vec{v_1} = \left(4,~7\right) $ and $ \vec{v_2} = \left(1,~-5\right) $ . | 1 |
| 3111 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~8\right) $ . | 1 |
| 3112 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~8\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 1 |
| 3113 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5,~3\right) $ . | 1 |
| 3114 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5,~6\right) $ . | 1 |
| 3115 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~4,~-2\right) $ and $ \vec{v_2} = \left(3,~-5,~-9\right) $ . | 1 |
| 3116 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-8,~5\right) $ and $ \vec{v_2} = \left(2,~-1,~7\right) $ . | 1 |
| 3117 | Find the angle between vectors $ \left(0,~5,~5\right)$ and $\left(3,~0,~-4\right)$. | 1 |
| 3118 | Find the angle between vectors $ \left(-4,~4,~0\right)$ and $\left(3,~10,~-4\right)$. | 1 |
| 3119 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~6,~-1\right) $ . | 1 |
| 3120 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~7\right) $ . | 1 |
| 3121 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(3,~-3\right) $ . | 1 |
| 3122 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~6,~4\right) $ . | 1 |
| 3123 | Find the difference of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(-3,~1\right) $ . | 1 |
| 3124 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~8,~-2\right) $ and $ \vec{v_2} = \left(8,~2,~-6\right) $ . | 1 |
| 3125 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~8,~-2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3126 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~2,~-6\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3127 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~0,~20\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3128 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-15,~5,~25\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3129 | Calculate the dot product of the vectors $ \vec{v_1} = \left(16,~-8,~-32\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3130 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~0\right) $ . | 1 |
| 3131 | Determine whether the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(3,~6\right) $ are linearly independent or dependent. | 1 |
| 3132 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~7\right) $ . | 1 |
| 3133 | Find the angle between vectors $ \left(-8,~7\right)$ and $\left(2,~-5\right)$. | 1 |
| 3134 | Determine whether the vectors $ \vec{v_1} = \left(\sqrt{ 2 },~-\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(\sqrt{ 5 },~0\right) $ are linearly independent or dependent. | 1 |
| 3135 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 5 }{ 2 },~\dfrac{ 5 }{ 2 },~1\right) $ and $ \vec{v_2} = \left(4,~6,~-9\right) $ . | 1 |
| 3136 | Find the difference of the vectors $ \vec{v_1} = \left(5,~-6\right) $ and $ \vec{v_2} = \left(7,~-3\right) $ . | 1 |
| 3137 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-12,~-15\right) $ . | 1 |
| 3138 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-12,~-15\right) $ . | 1 |
| 3139 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~10\right) $ and $ \vec{v_2} = \left(-12,~-3\right) $ . | 1 |
| 3140 | Find the sum of the vectors $ \vec{v_1} = \left(224,~52\right) $ and $ \vec{v_2} = \left(80,~40\right) $ . | 1 |
| 3141 | Find the difference of the vectors $ \vec{v_1} = \left(224,~52\right) $ and $ \vec{v_2} = \left(80,~40\right) $ . | 1 |
| 3142 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-32\right) $ . | 1 |
| 3143 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-32\right) $ and $ \vec{v_2} = \left(6,~-185\right) $ . | 1 |
| 3144 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~4\right) $ and $ \vec{v_2} = \left(9,~1\right) $ . | 1 |
| 3145 | Find the projection of the vector $ \vec{v_1} = \left(5,~-1\right) $ on the vector $ \vec{v_2} = \left(-1,~2\right) $. | 1 |
| 3146 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-5,~-7\right) $ . | 1 |
| 3147 | Find the angle between vectors $ \left(-7,~4\right)$ and $\left(5,~\dfrac{ 35 }{ 4 }\right)$. | 1 |
| 3148 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-9\right) $ and $ \vec{v_2} = \left(-7,~3\right) $ . | 1 |
| 3149 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-2\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 3150 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~3,~3\right) $ . | 1 |
