Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2101 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 13 }{ 5 },~\dfrac{ 9 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 27 }{ 10 },~-\dfrac{ 1 }{ 10 }\right) $ . | 2 |
2102 | Find the magnitude of the vector $ \| \vec{v} \| = \left(25,~0\right) $ . | 2 |
2103 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(-3,~-8\right) $ . | 2 |
2104 | Find the projection of the vector $ \vec{v_1} = \left(-2,~3,~1\right) $ on the vector $ \vec{v_2} = \left(1,~1,~2\right) $. | 2 |
2105 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 2 |
2106 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 2 |
2107 | Find the difference of the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ . | 2 |
2108 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-3\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ . | 2 |
2109 | Find the projection of the vector $ \vec{v_1} = \left(2345,~2234\right) $ on the vector $ \vec{v_2} = \left(4721,~4576\right) $. | 2 |
2110 | Find the difference of the vectors $ \vec{v_1} = \left(-27,~21\right) $ and $ \vec{v_2} = \left(-12,~4\right) $ . | 2 |
2111 | Find the projection of the vector $ \vec{v_1} = \left(3,~-2\right) $ on the vector $ \vec{v_2} = \left(5,~1\right) $. | 2 |
2112 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(6,~-4\right) $ . | 2 |
2113 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(-1,~-6\right) $ . | 2 |
2114 | Find the sum of the vectors $ \vec{v_1} = \left(32,~40\right) $ and $ \vec{v_2} = \left(42,~36\right) $ . | 2 |
2115 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~-\dfrac{ 707107 }{ 25000 }\right) $ . | 2 |
2116 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~1\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 2 |
2117 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~4\right) $ . | 2 |
2118 | Find the angle between vectors $ \left(-9,~1\right)$ and $\left(8,~5\right)$. | 2 |
2119 | Find the difference of the vectors $ \vec{v_1} = \left(-7,~-1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 2 |
2120 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-3,~-2\right) $ . | 2 |
2121 | Find the projection of the vector $ \vec{v_1} = \left(3,~4\right) $ on the vector $ \vec{v_2} = \left(6,~8\right) $. | 2 |
2122 | Find the difference of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 2 |
2123 | Find the angle between vectors $ \left(8,~4\right)$ and $\left(-2,~4\right)$. | 2 |
2124 | Find the projection of the vector $ \vec{v_1} = \left(-1,~8\right) $ on the vector $ \vec{v_2} = \left(9,~6\right) $. | 2 |
2125 | Find the angle between vectors $ \left(1,~3\right)$ and $\left(4,~-3\right)$. | 2 |
2126 | Find the magnitude of the vector $ \| \vec{v} \| = \left(74,~76\right) $ . | 2 |
2127 | Find the difference of the vectors $ \vec{v_1} = \left(5,~7\right) $ and $ \vec{v_2} = \left(-9,~28\right) $ . | 2 |
2128 | Find the sum of the vectors $ \vec{v_1} = \left(4,~4\right) $ and $ \vec{v_2} = \left(-2,~-2\right) $ . | 2 |
2129 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3,~5\right) $ and $ \vec{v_2} = \left(-2,~4,~-1\right) $ . | 2 |
2130 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(0,~-8\right) $ . | 2 |
2131 | Determine whether the vectors $ \vec{v_1} = \left(0,~2,~4\right) $, $ \vec{v_2} = \left(4,~0,~7\right) $ and $ \vec{v_3} = \left(4,~-2,~3\right)$ are linearly independent or dependent. | 2 |
2132 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-3\right) $ . | 2 |
2133 | Find the angle between vectors $ \left(24,~40\right)$ and $\left(40,~1\right)$. | 2 |
2134 | Find the angle between vectors $ \left(1,~3\right)$ and $\left(-4,~-3\right)$. | 2 |
2135 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ . | 2 |
2136 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~1\right) $ . | 2 |
2137 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-0.3846,~0.9231\right) $ . | 2 |
2138 | Find the projection of the vector $ \vec{v_1} = \left(-1,~3\right) $ on the vector $ \vec{v_2} = \left(4,~4\right) $. | 2 |
2139 | Find the sum of the vectors $ \vec{v_1} = \left(-190,~321\right) $ and $ \vec{v_2} = \left(230,~80\right) $ . | 2 |
2140 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 13 }{ 5 },~\dfrac{ 9 }{ 2 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 13 }{ 5 },~\dfrac{ 22 }{ 5 }\right) $ . | 2 |
2141 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ . | 2 |
2142 | Find the angle between vectors $ \left(5,~-1\right)$ and $\left(4,~6\right)$. | 2 |
2143 | Find the angle between vectors $ \left(6,~-8\right)$ and $\left(-1,~8\right)$. | 2 |
2144 | Find the angle between vectors $ \left(40,~25\right)$ and $\left(24,~1\right)$. | 2 |
2145 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ . | 2 |
2146 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(7,~2\right) $ . | 2 |
2147 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 2 |
2148 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-6\right) $ and $ \vec{v_2} = \left(2,~-1,~3\right) $ . | 2 |
2149 | Find the difference of the vectors $ \vec{v_1} = \left(10,~-4\right) $ and $ \vec{v_2} = \left(0,~-1\right) $ . | 2 |
2150 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 2 |