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
1501	Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~8,~9\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ .	2
1502	Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(0,~-5\right) $ .	2
1503	Find the sum of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(-5,~0\right) $ .	2
1504	Find the sum of the vectors $ \vec{v_1} = \left(0,~34\right) $ and $ \vec{v_2} = \left(34,~0\right) $ .	2
1505	Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~6\right) $ and $ \vec{v_2} = \left(-5,~9\right) $ .	2
1506	Find the projection of the vector $ \vec{v_1} = \left(-2,~4\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $.	2
1507	Determine whether the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(0,~0\right) $ are linearly independent or dependent.	2
1508	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0.1111,~0.8889\right) $ .	2
1509	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(10,~12\right) $ .	2
1510	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(10,~12\right) $ .	2
1511	Find the difference of the vectors $ \vec{v_1} = \left(10,~12\right) $ and $ \vec{v_2} = \left(4,~20\right) $ .	2
1512	Find the angle between vectors $ \left(-6,~13\right)$ and $\left(1,~0\right)$.	2
1513	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-6,~13\right) $ .	2
1514	Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~13\right) $ and $ \vec{v_2} = \left(-42,~-34\right) $ .	2
1515	Find the difference of the vectors $ \vec{v_1} = \left(330,~0\right) $ and $ \vec{v_2} = \left(170,~-120\right) $ .	2
1516	Find the difference of the vectors $ \vec{v_1} = \left(330,~0\right) $ and $ \vec{v_2} = \left(175,~-120\right) $ .	2
1517	Find the difference of the vectors $ \vec{v_1} = \left(330,~0\right) $ and $ \vec{v_2} = \left(200,~-120\right) $ .	2
1518	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~1,~-3\right) $ .	2
1519	Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~0,~4\right) $ and $ \vec{v_2} = \left(-2,~2,~1\right) $ .	2
1520	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 8 }{ 9 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right) $ .	2
1521	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 8 }{ 9 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right) $ .	2
1522	Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 8 }{ 9 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right) $ are linearly independent or dependent.	2
1523	Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 8 }{ 9 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right) $ .	2
1524	Find the angle between vectors $ \left(\dfrac{ 1 }{ 9 },~\dfrac{ 8 }{ 9 }\right)$ and $\left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right)$.	2
1525	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ .	2
1526	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 3 }{ 4 }\right) $ .	2
1527	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 3 }{ 4 }\right) $ .	2
1528	Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 3 }{ 4 }\right) $ .	2
1529	Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 3 }{ 4 }\right) $ are linearly independent or dependent.	2
1530	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~17\right) $ .	2
1531	Find the angle between vectors $ \left(16,~-6\right)$ and $\left(3,~1\right)$.	2
1532	Find the sum of the vectors $ \vec{v_1} = \left(8,~4\right) $ and $ \vec{v_2} = \left(-3,~-1\right) $ .	2
1533	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~3\right) $ .	2
1534	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~2,~3\right) $ .	2
1535	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~1\right) $ .	2
1536	Find the difference of the vectors $ \vec{v_1} = \left(-3,~0\right) $ and $ \vec{v_2} = \left(5,~0\right) $ .	2
1537	Find the angle between vectors $ \left(30,~0\right)$ and $\left(47,~0\right)$.	2
1538	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3090,~-2954\right) $ .	2
1539	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~9\right) $ .	2
1540	Find the sum of the vectors $ \vec{v_1} = \left(2,~9\right) $ and $ \vec{v_2} = \left(9,~0\right) $ .	2
1541	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~5\right) $ .	2
1542	Find the difference of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ .	2
1543	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ .	2
1544	Find the sum of the vectors $ \vec{v_1} = \left(-1,~-4,~2\right) $ and $ \vec{v_2} = \left(3,~3,~-2\right) $ .	2
1545	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(2,~-1,~0\right) $ .	2
1546	Find the sum of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(7,~-1\right) $ .	2
1547	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~2,~1\right) $ .	2
1548	Find the sum of the vectors $ \vec{v_1} = \left(-48,~64\right) $ and $ \vec{v_2} = \left(54,~27\right) $ .	2
1549	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~8\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ .	2
1550	Find the angle between vectors $ \left(3,~-2\right)$ and $\left(-3,~7\right)$.	2