Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5901 | Find the difference of the vectors $ \vec{v_1} = \left(132163,~20000,~15950\right) $ and $ \vec{v_2} = \left(131372,~20869,~13724\right) $ . | 1 |
5902 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-4,~1\right) $ and $ \vec{v_2} = \left(-10,~5,~10\right) $ . | 1 |
5903 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-5,~1\right) $ and $ \vec{v_2} = \left(6,~-5,~1\right) $ . | 1 |
5904 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-2\right) $ . | 1 |
5905 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
5906 | Find the angle between vectors $ \left(1,~2,~-2\right)$ and $\left(2,~1,~1\right)$. | 1 |
5907 | Find the angle between vectors $ \left(-4,~8,~10\right)$ and $\left(5,~1,~-3\right)$. | 1 |
5908 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0,~0\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
5909 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-2 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(6,~-2 \sqrt{ 3 }\right) $ . | 1 |
5910 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-12\right) $ and $ \vec{v_2} = \left(-30,~24\right) $ . | 1 |
5911 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~-3\right) $ . | 1 |
5912 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~7,~3\right) $ and $ \vec{v_2} = \left(4,~2,~-4\right) $ . | 1 |
5913 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 1 |
5914 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2.5,~0.6\right) $ and $ \vec{v_2} = \left(-6,~4\right) $ . | 1 |
5915 | Find the difference of the vectors $ \vec{v_1} = \left(3,~12\right) $ and $ \vec{v_2} = \left(0,~6\right) $ . | 1 |
5916 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 259 }{ 100 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(0,~3\right) $ . | 1 |
5917 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 1 |
5918 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 353 }{ 40 },~\dfrac{ 1257 }{ 1000 },~-\dfrac{ 3 }{ 200 }\right) $ . | 1 |
5919 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-3\right) $ . | 1 |
5920 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 17 }{ 5 },~\dfrac{ 271 }{ 100 }\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 87 }{ 20 }\right) $ . | 1 |
5921 | Find the projection of the vector $ \vec{v_1} = \left(5,~6\right) $ on the vector $ \vec{v_2} = \left(8,~1\right) $. | 1 |
5922 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1,~-2\right) $ . | 1 |
5923 | Determine whether the vectors $ \vec{v_1} = \left(15,~-8\right) $ and $ \vec{v_2} = \left(-5,~12\right) $ are linearly independent or dependent. | 1 |
5924 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-4\right) $ and $ \vec{v_2} = \left(6,~-5,~1\right) $ . | 1 |
5925 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~0,~-2\right) $ and $ \vec{v_2} = \left(3,~0,~-2\right) $ . | 1 |
5926 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~4,~2\right) $ and $ \vec{v_2} = \left(0,~1,~-6\right) $ . | 1 |
5927 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
5928 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~5,~6\right) $ and $ \vec{v_2} = \left(-3,~5,~6\right) $ . | 1 |
5929 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~3,~-4\right) $ and $ \vec{v_2} = \left(1,~1,~-7\right) $ . | 1 |
5930 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~8\right) $ . | 1 |
5931 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 27 }{ 5 },~\dfrac{ 83 }{ 10 },~-\dfrac{ 47 }{ 5 }\right) $ . | 1 |
5932 | Find the angle between vectors $ \left(4,~4,~8\right)$ and $\left(2,~2,~1\right)$. | 1 |
5933 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 69503 }{ 100000 },~0.0652,~\dfrac{ 30519 }{ 3125 }\right) $ on the vector $ \vec{v_2} = \left(0,~0,~\dfrac{ 49 }{ 5 }\right) $. | 1 |
5934 | Find the sum of the vectors $ \vec{v_1} = \left(0,~3,~-4\right) $ and $ \vec{v_2} = \left(2,~4,~7\right) $ . | 1 |
5935 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(-8,~5,~6\right) $ . | 1 |
5936 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~1\right) $ . | 1 |
5937 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(-3,~0\right) $ . | 1 |
5938 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $ and $ \vec{v_2} = \left(-1,~-1,~5\right) $ . | 1 |
5939 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~3\right) $ and $ \vec{v_2} = \left(-5,~4\right) $ . | 1 |
5940 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-2,~-4\right) $ and $ \vec{v_2} = \left(1,~-1,~-2\right) $ . | 1 |
5941 | Find the sum of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(7,~3\right) $ . | 1 |
5942 | Determine whether the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(-9,~7\right) $ are linearly independent or dependent. | 1 |
5943 | Find the difference of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 87 }{ 20 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 17 }{ 5 },~\dfrac{ 271 }{ 100 }\right) $ . | 1 |
5944 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-1,~-2\right) $ . | 1 |
5945 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-4,~-3\right) $ and $ \vec{v_2} = \left(6,~-5,~1\right) $ . | 1 |
5946 | Find the angle between vectors $ \left(1,~-1,~1\right)$ and $\left(-1,~0,~1\right)$. | 1 |
5947 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~8,~10\right) $ and $ \vec{v_2} = \left(4,~2,~-6\right) $ . | 1 |
5948 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2\right) $ . | 1 |
5949 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~12\right) $ . | 1 |
5950 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(-3,~-3\right) $ . | 1 |