Vectors

(the database of solved problems)

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

Select category

ID	Problem	Count
2251	Find the difference of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(3,~5\right) $ .	2
2252	Find the angle between vectors $ \left(6,~1\right)$ and $\left(4,~2\right)$.	2
2253	Determine whether the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(8,~-6\right) $ are linearly independent or dependent.	2
2254	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 4 }{ 5 },~-\dfrac{ 8 }{ 5 }\right) $ and $ \vec{v_2} = \left(4,~2\right) $ .	2
2255	Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(-7,~2\right) $ .	2
2256	Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(7,~2\right) $ .	2
2257	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-5,~-4\right) $ .	2
2258	Find the projection of the vector $ \vec{v_1} = \left(3,~3\right) $ on the vector $ \vec{v_2} = \left(5,~1\right) $.	2
2259	Find the projection of the vector $ \vec{v_1} = \left(3,~6\right) $ on the vector $ \vec{v_2} = \left(8,~-4\right) $.	2
2260	Find the projection of the vector $ \vec{v_1} = \left(-1,~-2\right) $ on the vector $ \vec{v_2} = \left(0,~5\right) $.	2
2261	Find the angle between vectors $ \left(-1,~-2\right)$ and $\left(0,~5\right)$.	2
2262	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ .	2
2263	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(- \dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right) $ .	2
2264	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 2 },~\dfrac{ 31 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 22 }{ 5 },~\dfrac{ 73 }{ 10 }\right) $ .	2
2265	Find the angle between vectors $ \left(- \dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right)$ and $\left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right)$.	2
2266	Find the sum of the vectors $ \vec{v_1} = \left(-2,~5\right) $ and $ \vec{v_2} = \left(4,~2\right) $ .	2
2267	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(11,~11 \sqrt{ 3 }\right) $ .	2
2268	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-3\right) $ and $ \vec{v_2} = \left(-7,~5\right) $ .	2
2269	Find the projection of the vector $ \vec{v_1} = \left(0,~0,~0\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $.	2
2270	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~5\right) $ .	2
2271	Find the sum of the vectors $ \vec{v_1} = \left(4,~8\right) $ and $ \vec{v_2} = \left(4,~-7\right) $ .	2
2272	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~1\right) $ and $ \vec{v_2} = \left(8,~1\right) $ .	2
2273	Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(-3,~-1\right) $ .	2
2274	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-7,~-8\right) $ .	2
2275	Calculate the dot product of the vectors $ \vec{v_1} = \left(-\sqrt{ 3 },~-4\right) $ and $ \vec{v_2} = \left(-1,~4 \sqrt{ 3 }\right) $ .	2
2276	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~1\right) $ .	2
2277	Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~1\right) $ and $ \vec{v_2} = \left(1,~6\right) $ .	2
2278	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ .	2
2279	Find the difference of the vectors $ \vec{v_1} = \left(-8,~-6\right) $ and $ \vec{v_2} = \left(9,~7\right) $ .	2
2280	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(9,~-8\right) $ .	2
2281	Find the difference of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-4,~1\right) $ .	2
2282	Find the difference of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(6,~4\right) $ .	2
2283	Find the difference of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(0,~2\right) $ .	2
2284	Find the sum of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-4,~6\right) $ .	2
2285	Find the difference of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(18,~-9\right) $ .	2
2286	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~0\right) $ and $ \vec{v_2} = \left(1,~0,~7\right) $ .	2
2287	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~0\right) $ and $ \vec{v_2} = \left(9,~9\right) $ .	2
2288	Find the angle between vectors $ \left(3,~0\right)$ and $\left(9,~9\right)$.	2
2289	Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(5,~3\right) $ .	2
2290	Find the angle between vectors $ \left(9,~-3\right)$ and $\left(5,~3\right)$.	2
2291	Find the difference of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(3,~3\right) $ .	2
2292	Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~-2\right) $ and $ \vec{v_2} = \left(0,~2,~5\right) $ .	2
2293	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~2\right) $ and $ \vec{v_2} = \left(3,~2,~-2\right) $ .	2
2294	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-\dfrac{ 6 }{ 5 }\right) $ .	2
2295	Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(-3,~9\right) $ .	2
2296	Find the angle between vectors $ \left(-1,~1\right)$ and $\left(3,~-3\right)$.	2
2297	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~4\right) $ .	2
2298	Find the angle between vectors $ \left(200,~0\right)$ and $\left(0,~20\right)$.	2
2299	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(200,~0\right) $ .	2
2300	Calculate the dot product of the vectors $ \vec{v_1} = \left(200,~0\right) $ and $ \vec{v_2} = \left(0,~20\right) $ .	2