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
2301	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~4\right) $ .	2
2302	Find the angle between vectors $ \left(4,~4\right)$ and $\left(8,~-2\right)$.	2
2303	Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~-4\right) $ and $ \vec{v_2} = \left(-3,~-4,~-5\right) $ .	2
2304	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~12\right) $ .	2
2305	Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 4 }\right) $ .	2
2306	Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ .	2
2307	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ .	2
2308	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(5,~0\right) $ .	2
2309	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~0\right) $ and $ \vec{v_2} = \left(4,~-9\right) $ .	2
2310	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~6\right) $ and $ \vec{v_2} = \left(2,~3\right) $ .	2
2311	Find the difference of the vectors $ \vec{v_1} = \left(8,~9\right) $ and $ \vec{v_2} = \left(9,~7\right) $ .	2
2312	Find the projection of the vector $ \vec{v_1} = \left(-2,~2\right) $ on the vector $ \vec{v_2} = \left(0,~-4\right) $.	2
2313	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~-4\right) $ .	2
2314	Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(2,~-7\right) $ .	2
2315	Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-7,~-2\right) $ .	2
2316	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(4,~5,~6\right) $ .	2
2317	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~2\right) $ and $ \vec{v_2} = \left(-1,~5,~-2\right) $ .	2
2318	Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~2\right) $ and $ \vec{v_2} = \left(-1,~5,~-2\right) $ .	2
2319	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~6\right) $ .	2
2320	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 87 }{ 10 },~5\right) $ and $ \vec{v_2} = \left(\dfrac{ 43 }{ 10 },~\dfrac{ 5 }{ 2 }\right) $ .	2
2321	Find the angle between vectors $ \left(\dfrac{ 87 }{ 10 },~5\right)$ and $\left(\dfrac{ 43 }{ 10 },~\dfrac{ 5 }{ 2 }\right)$.	2
2322	Find the angle between vectors $ \left(2,~5\right)$ and $\left(5,~-2\right)$.	2
2323	Calculate the dot product of the vectors $ \vec{v_1} = \left(\sqrt{ 3 },~3\right) $ and $ \vec{v_2} = \left(1,~1\right) $ .	2
2324	Find the angle between vectors $ \left(\sqrt{ 3 },~3\right)$ and $\left(1,~1\right)$.	2
2325	Find the projection of the vector $ \vec{v_1} = \left(\sqrt{ 3 },~-1\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $.	2
2326	Find the projection of the vector $ \vec{v_1} = \left(\sqrt{ 3 },~-1\right) $ on the vector $ \vec{v_2} = \left(-1,~1\right) $.	2
2327	Find the angle between vectors $ \left(\sqrt{ 3 },~-1\right)$ and $\left(-1,~1\right)$.	2
2328	Find the angle between vectors $ \left(-\sqrt{ 3 },~-1\right)$ and $\left(-1,~1\right)$.	2
2329	Find the angle between vectors $ \left(\sqrt{ 3 },~-3\right)$ and $\left(1,~-1\right)$.	2
2330	Calculate the dot product of the vectors $ \vec{v_1} = \left(\sqrt{ 3 },~-3\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ .	2
2331	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ .	2
2332	Find the angle between vectors $ \left(-3,~0\right)$ and $\left(1,~0\right)$.	2
2333	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-6,~-4\right) $ .	2
2334	Find the projection of the vector $ \vec{v_1} = \left(7.07,~7.07\right) $ on the vector $ \vec{v_2} = \left(2.99,~7.42\right) $.	2
2335	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~-2\right) $ .	2
2336	Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(5,~4\right) $ .	2
2337	Find the sum of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(5,~4\right) $ .	2
2338	Find the difference of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(5,~4\right) $ .	2
2339	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ .	2
2340	Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ .	2
2341	Find the angle between vectors $ \left(6,~11\right)$ and $\left(3,~4\right)$.	2
2342	Find the angle between vectors $ \left(5,~-5\right)$ and $\left(-4,~-3\right)$.	2
2343	Find the angle between vectors $ \left(-5,~0\right)$ and $\left(4,~-2\right)$.	2
2344	Find the angle between vectors $ \left(-5,~3\right)$ and $\left(4,~-2\right)$.	2
2345	Find the angle between vectors $ \left(-1,~-5\right)$ and $\left(5,~1\right)$.	2
2346	Find the angle between vectors $ \left(4,~2\right)$ and $\left(-5,~1\right)$.	2
2347	Find the angle between vectors $ \left(1,~3\right)$ and $\left(4,~-3\right)$.	2
2348	Find the angle between vectors $ \left(1,~3\right)$ and $\left(-4,~-3\right)$.	2
2349	Find the angle between vectors $ \left(-5,~-1\right)$ and $\left(-5,~-1\right)$.	2
2350	Find the angle between vectors $ \left(1,~-4\right)$ and $\left(-2,~0\right)$.	2