Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
51 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~2\right) $ . | 5 |
52 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 5 |
53 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 5 |
54 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~3\right) $ . | 5 |
55 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-9\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ . | 5 |
56 | Find the angle between vectors $ \left(4,~3\right)$ and $\left(2,~3\right)$. | 5 |
57 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~0\right) $ . | 5 |
58 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 5 |
59 | Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(10,~5\right) $. | 5 |
60 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-15,~-45\right) $ . | 5 |
61 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~3\right) $ . | 5 |
62 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~12\right) $ . | 5 |
63 | Find the angle between vectors $ \left(-78,~44\right)$ and $\left(87,~80\right)$. | 5 |
64 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~3\right) $ . | 5 |
65 | Find the difference of the vectors $ \vec{v_1} = \left(9,~5\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 5 |
66 | Find the difference of the vectors $ \vec{v_1} = \left(10,~-1\right) $ and $ \vec{v_2} = \left(10,~-4\right) $ . | 5 |
67 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(1,~-1\right)$. | 5 |
68 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 5 |
69 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ . | 5 |
70 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 21 }{ 10 },~-\dfrac{ 16 }{ 5 }\right) $ . | 5 |
71 | Find the difference of the vectors $ \vec{v_1} = \left(7,~1\right) $ and $ \vec{v_2} = \left(5,~5\right) $ . | 5 |
72 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 5 |
73 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(28,~-49\right) $ . | 5 |
74 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(5,~29\right) $ . | 5 |
75 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-12\right) $ . | 5 |
76 | Find the projection of the vector $ \vec{v_1} = \left(2,~-6\right) $ on the vector $ \vec{v_2} = \left(-\dfrac{ 1 }{ 3 },~\dfrac{ 3 }{ 5 }\right) $. | 5 |
77 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-3\right) $ . | 5 |
78 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 5 |
79 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0\right) $ . | 5 |
80 | Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 5 |
81 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 5 |
82 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 70707 }{ 1000 },~\dfrac{ 16853 }{ 200 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 28191 }{ 500 },~\dfrac{ 20521 }{ 1000 }\right) $ . | 5 |
83 | Find the angle between vectors $ \left(5,~-3\right)$ and $\left(-8,~8\right)$. | 5 |
84 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-2\right) $ . | 5 |
85 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(4,~5,~6\right) $ . | 5 |
86 | Find the projection of the vector $ \vec{v_1} = \left(8,~5\right) $ on the vector $ \vec{v_2} = \left(-9,~-2\right) $. | 4 |
87 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0.8,~0.2\right) $ and $ \vec{v_2} = \left(0.35,~0.65\right) $ . | 4 |
88 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~0\right) $ . | 4 |
89 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~7\right) $ . | 4 |
90 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(-9,~3\right)$. | 4 |
91 | Find the projection of the vector $ \vec{v_1} = \left(3,~-5\right) $ on the vector $ \vec{v_2} = \left(0,~1\right) $. | 4 |
92 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 4 |
93 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 4 |
94 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 4 |
95 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(8,~-2\right) $ . | 4 |
96 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 29 }{ 10 },~\dfrac{ 307 }{ 100 }\right) $ and $ \vec{v_2} = \left(240,~300\right) $ . | 4 |
97 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 4 |
98 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-16\right) $ and $ \vec{v_2} = \left(8,~-20\right) $ . | 4 |
99 | Find the angle between vectors $ \left(\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 10 }\right)$ and $\left(-\dfrac{ 3 }{ 20 },~\dfrac{ 1 }{ 5 }\right)$. | 4 |
100 | Find the difference of the vectors $ \vec{v_1} = \left(-24,~21\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 4 |