Vectors

(the database of solved problems)

All the problems and solutions shown below were generated using the Vectors Calculator.

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ID	Problem	Count
2201	Find the sum of the vectors $ \vec{v_1} = \left(8,~7\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ .	2
2202	Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~4\right) $ and $ \vec{v_2} = \left(-6,~2\right) $ .	2
2203	Find the sum of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(5,~4\right) $ .	2
2204	Find the difference of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(5,~4\right) $ .	2
2205	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 10 },~\dfrac{ 7 }{ 10 }\right) $ .	2
2206	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ .	2
2207	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ .	2
2208	Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ .	2
2209	Find the angle between vectors $ \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right)$ and $\left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right)$.	2
2210	Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ are linearly independent or dependent.	2
2211	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 10 },~\dfrac{ 7 }{ 10 }\right) $ .	2
2212	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1210,~0\right) $ .	2
2213	Find the sum of the vectors $ \vec{v_1} = \left(1210,~0\right) $ and $ \vec{v_2} = \left(395.993,~1477.87\right) $ .	2
2214	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(5,~2\right) $ .	2
2215	Find the angle between vectors $ \left(0,~4\right)$ and $\left(-4,~3\right)$.	2
2216	Find the projection of the vector $ \vec{v_1} = \left(-1,~8\right) $ on the vector $ \vec{v_2} = \left(9,~6\right) $.	2
2217	Find the projection of the vector $ \vec{v_1} = \left(-4,~-7\right) $ on the vector $ \vec{v_2} = \left(3,~-8\right) $.	2
2218	Find the projection of the vector $ \vec{v_1} = \left(-2,~6\right) $ on the vector $ \vec{v_2} = \left(1,~6\right) $.	2
2219	Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(1,~4\right) $ .	2
2220	Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ .	2
2221	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~3\right) $ and $ \vec{v_2} = \left(4,~2\right) $ .	2
2222	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\sqrt{ 2 },~-\dfrac{ 1 }{ 2 }\right) $ .	2
2223	Find the angle between vectors $ \left(5,~-1\right)$ and $\left(3,~1\right)$.	2
2224	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~6\right) $ .	2
2225	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~7\right) $ .	2
2226	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(1,~3\right) $ .	2
2227	Find the angle between vectors $ \left(5,~2\right)$ and $\left(-5,~2\right)$.	2
2228	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(1,~0,~3\right) $ .	2
2229	Find the angle between vectors $ \left(8,~6\right)$ and $\left(3,~-4\right)$.	2
2230	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~-23\right) $ .	2
2231	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-7,~-5\right) $ .	2
2232	Find the sum of the vectors $ \vec{v_1} = \left(-2,~7\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ .	2
2233	Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(-4,~-4\right) $ .	2
2234	Determine whether the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(2,~3\right) $ are linearly independent or dependent.	2
2235	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(250,~140\right) $ .	2
2236	Find the sum of the vectors $ \vec{v_1} = \left(3,~-9\right) $ and $ \vec{v_2} = \left(8,~4\right) $ .	2
2237	Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(7,~2\right) $ .	2
2238	Find the sum of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ .	2
2239	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-7\right) $ .	2
2240	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-5,~4\right) $ .	2
2241	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(5,~7\right) $ .	2
2242	Find the angle between vectors $ \left(4,~5\right)$ and $\left(6,~7\right)$.	2
2243	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
2244	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
2245	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~\sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(-1,~\sqrt{ 3 }\right) $ .	2
2246	Find the projection of the vector $ \vec{v_1} = \left(1,~\sqrt{ 3 }\right) $ on the vector $ \vec{v_2} = \left(-1,~\sqrt{ 3 }\right) $.	2
2247	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~7\right) $ .	2
2248	Find the angle between vectors $ \left(1,~\sqrt{ 3 }\right)$ and $\left(-1,~\sqrt{ 3 }\right)$.	2
2249	Find the difference of the vectors $ \vec{v_1} = \left(1,~\sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ .	2
2250	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(-1,~\sqrt{ 3 }\right) $ .	2