Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3051 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~35\right) $ and $ \vec{v_2} = \left(60,~-11\right) $ . | 1 |
| 3052 | Find the projection of the vector $ \vec{v_1} = \left(3,~5\right) $ on the vector $ \vec{v_2} = \left(7,~2\right) $. | 1 |
| 3053 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 1 |
| 3054 | Find the sum of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 1 |
| 3055 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2 \sqrt{ 2 },~-2,~2\right) $ and $ \vec{v_2} = \left(2,~-1,~3\right) $ . | 1 |
| 3056 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-10\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ . | 1 |
| 3057 | Find the projection of the vector $ \vec{v_1} = \left(3,~-5\right) $ on the vector $ \vec{v_2} = \left(-6,~10\right) $. | 1 |
| 3058 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~1\right) $ . | 1 |
| 3059 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~-4\right) $ and $ \vec{v_2} = \left(-3,~4,~2\right) $ . | 1 |
| 3060 | Find the projection of the vector $ \vec{v_1} = \left(-1,~11\right) $ on the vector $ \vec{v_2} = \left(-8,~15\right) $. | 1 |
| 3061 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3,~-8\right) $ and $ \vec{v_2} = \left(4,~-5,~4\right) $ . | 1 |
| 3062 | Find the angle between vectors $ \left(1,~3,~-8\right)$ and $\left(4,~-5,~4\right)$. | 1 |
| 3063 | Determine whether the vectors $ \vec{v_1} = \left(1,~8,~-1\right) $, $ \vec{v_2} = \left(6,~5,~2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 3064 | Find the projection of the vector $ \vec{v_1} = \left(-1,~3\right) $ on the vector $ \vec{v_2} = \left(-1,~-2\right) $. | 1 |
| 3065 | Find the difference of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-1,~-2\right) $ . | 1 |
| 3066 | Find the projection of the vector $ \vec{v_1} = \left(0.3162,~0.9487\right) $ on the vector $ \vec{v_2} = \left(-1,~-2\right) $. | 1 |
| 3067 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 4427 }{ 5000 },~\dfrac{ 4427 }{ 2500 }\right) $ and $ \vec{v_2} = \left(-1,~-2\right) $ . | 1 |
| 3068 | Find the magnitude of the vector $ \| \vec{v} \| = \left(24,~27\right) $ . | 1 |
| 3069 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(2,~-4\right) $ . | 1 |
| 3070 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~0\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 3071 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-59,~-119\right) $ . | 1 |
| 3072 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-1,~2\right) $ . | 1 |
| 3073 | Find the angle between vectors $ \left(1,~0\right)$ and $\left(\dfrac{\sqrt{ 3 }}{ 2 },~\dfrac{ 1 }{ 2 }\right)$. | 1 |
| 3074 | Find the angle between vectors $ \left(1,~0\right)$ and $\left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right)$. | 1 |
| 3075 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(3,~3\right) $ . | 1 |
| 3076 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 2067 }{ 100 },~-\dfrac{ 777 }{ 20 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 3657 }{ 100 },~\dfrac{ 1009 }{ 100 }\right) $ . | 1 |
| 3077 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(0,~2,~2\right) $ . | 1 |
| 3078 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~4,~0\right) $ and $ \vec{v_2} = \left(-3,~0,~9\right) $ . | 1 |
| 3079 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~4,~-1\right) $ and $ \vec{v_2} = \left(-3,~0,~9\right) $ . | 1 |
| 3080 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~4\right) $ and $ \vec{v_2} = \left(2,~-6,~0\right) $ . | 1 |
| 3081 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-6,~10\right) $ and $ \vec{v_2} = \left(1,~-3,~-5\right) $ . | 1 |
| 3082 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-10,~11\right) $ . | 1 |
| 3083 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~5\right) $ . | 1 |
| 3084 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~2\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
| 3085 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-10,~11\right) $ and $ \vec{v_2} = \left(3,~0,~-4\right) $ . | 1 |
| 3086 | Find the angle between vectors $ \left(2,~-10,~11\right)$ and $\left(3,~0,~-4\right)$. | 1 |
| 3087 | Find the difference of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 1 |
| 3088 | Find the difference of the vectors $ \vec{v_1} = \left(0,~\sqrt{ 5 }\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 1 |
| 3089 | Find the difference of the vectors $ \vec{v_1} = \left(2,~1,~-1\right) $ and $ \vec{v_2} = \left(4,~3,~-2\right) $ . | 1 |
| 3090 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~6\right) $ and $ \vec{v_2} = \left(-6,~4\right) $ . | 1 |
| 3091 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~13\right) $ . | 1 |
| 3092 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~2\right) $ . | 1 |
| 3093 | Find the sum of the vectors $ \vec{v_1} = \left(0,~6\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ . | 1 |
| 3094 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-8,~-4\right) $ and $ \vec{v_2} = \left(-1,~-4,~-4\right) $ . | 1 |
| 3095 | Find the sum of the vectors $ \vec{v_1} = \left(10,~-8\right) $ and $ \vec{v_2} = \left(4,~6\right) $ . | 1 |
| 3096 | Find the angle between vectors $ \left(3,~-4,~-5\right)$ and $\left(3,~4,~-5\right)$. | 1 |
| 3097 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-5,~3\right) $ . | 1 |
| 3098 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3,~-2\right) $ . | 1 |
| 3099 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~9,~-6\right) $ . | 1 |
| 3100 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1,~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(-2,~3,~-2\right) $ . | 1 |
