Vectors

(the database of solved problems)

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

Select category

ID	Problem	Count
1351	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~6\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ .	2
1352	Find the sum of the vectors $ \vec{v_1} = \left(-10,~12\right) $ and $ \vec{v_2} = \left(5,~-10\right) $ .	2
1353	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(50,~70\right) $ .	2
1354	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~3\right) $ .	2
1355	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right) $ .	2
1356	Find the angle between vectors $ \left(\dfrac{ 3 }{ 5 },~\dfrac{ 1 }{ 5 }\right)$ and $\left(\dfrac{ 2 }{ 5 },~\dfrac{ 4 }{ 5 }\right)$.	2
1357	Find the difference of the vectors $ \vec{v_1} = \left(-27,~21\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ .	2
1358	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 12 }{ 25 },~\dfrac{ 13 }{ 25 }\right) $ .	2
1359	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 9 }{ 10 },~\dfrac{ 1 }{ 10 }\right) $ .	2
1360	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~4\right) $ .	2
1361	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(295.4,~52.1\right) $ .	2
1362	Determine whether the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~2\right) $ are linearly independent or dependent.	2
1363	Find the angle between vectors $ \left(-2 \sqrt{ 3 },~-2\right)$ and $\left(-4,~-4 \sqrt{ 3 }\right)$.	2
1364	Find the angle between vectors $ \left(3,~4\right)$ and $\left(-2,~5\right)$.	2
1365	Find the projection of the vector $ \vec{v_1} = \left(5,~-3\right) $ on the vector $ \vec{v_2} = \left(13,~8\right) $.	2
1366	Find the difference of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ .	2
1367	Find the difference of the vectors $ \vec{v_1} = \left(-5,~-10\right) $ and $ \vec{v_2} = \left(12,~7\right) $ .	2
1368	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-9\right) $ and $ \vec{v_2} = \left(4,~12\right) $ .	2
1369	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~6\right) $ .	2
1370	Find the angle between vectors $ \left(-1,~6\right)$ and $\left(2,~-3\right)$.	2
1371	Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~1\right) $ and $ \vec{v_2} = \left(3,~-5\right) $ .	2
1372	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~8\right) $ .	2
1373	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~11\right) $ .	2
1374	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(-2,~0\right) $ .	2
1375	Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ .	2
1376	Find the angle between vectors $ \left(3,~8\right)$ and $\left(-2,~\dfrac{ 3 }{ 2 }\right)$.	2
1377	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 46 }{ 5 },~\dfrac{ 71 }{ 10 }\right) $ .	2
1378	Find the projection of the vector $ \vec{v_1} = \left(-10,~-4\right) $ on the vector $ \vec{v_2} = \left(4,~-3\right) $.	2
1379	Find the difference of the vectors $ \vec{v_1} = \left(4,~-5\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ .	2
1380	Find the projection of the vector $ \vec{v_1} = \left(0,~-2,~-1\right) $ on the vector $ \vec{v_2} = \left(-64,~-2,~30\right) $.	2
1381	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ .	2
1382	Find the angle between vectors $ \left(3,~-1\right)$ and $\left(-2,~5\right)$.	2
1383	Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~2\right) $ .	2
1384	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~8\right) $ .	2
1385	Find the difference of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~4\right) $ .	2
1386	Find the difference of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ .	2
1387	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~-6\right) $ .	2
1388	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~2\right) $ .	2
1389	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~5\right) $ .	2
1390	Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 1 }{ 8 },~\dfrac{ 7 }{ 8 }\right) $.	2
1391	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-5,~-2\right) $ .	2
1392	Find the angle between vectors $ \left(-8,~9\right)$ and $\left(5,~-2\right)$.	2
1393	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~-6\right) $ .	2
1394	Find the angle between vectors $ \left(-3,~-6\right)$ and $\left(-5,~2\right)$.	2
1395	Determine whether the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(4,~-2\right) $ are linearly independent or dependent.	2
1396	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ .	2
1397	Find the angle between vectors $ \left(0,~1\right)$ and $\left(0,~5\right)$.	2
1398	Find the projection of the vector $ \vec{v_1} = \left(-3,~4\right) $ on the vector $ \vec{v_2} = \left(6,~8\right) $.	2
1399	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(7,~8\right) $ .	2
1400	Find the angle between vectors $ \left(-1,~-3\right)$ and $\left(-2,~-3\right)$.	2