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
1001	Find the projection of the vector $ \vec{v_1} = \left(3,~4\right) $ on the vector $ \vec{v_2} = \left(6,~8\right) $.	2
1002	Find the difference of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(3,~4\right) $ .	2
1003	Find the sum of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(0,~-8\right) $ .	2
1004	Find the angle between vectors $ \left(0,~4\right)$ and $\left(\dfrac{ 3 \sqrt{ 2}}{ 2 },~\dfrac{ 3 \sqrt{ 2}}{ 2 }\right)$.	2
1005	Find the difference of the vectors $ \vec{v_1} = \left(3,~-8\right) $ and $ \vec{v_2} = \left(7,~\dfrac{ 21 }{ 8 }\right) $ .	2
1006	Find the sum of the vectors $ \vec{v_1} = \left(7,~-4\right) $ and $ \vec{v_2} = \left(-8,~9\right) $ .	2
1007	Find the difference of the vectors $ \vec{v_1} = \left(-27,~24\right) $ and $ \vec{v_2} = \left(5,~-40\right) $ .	2
1008	Find the difference of the vectors $ \vec{v_1} = \left(-27,~24\right) $ and $ \vec{v_2} = \left(-5,~-40\right) $ .	2
1009	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-7,~-4\right) $ .	2
1010	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(7,~-24\right) $ .	2
1011	Find the difference of the vectors $ \vec{v_1} = \left(28,~-1\right) $ and $ \vec{v_2} = \left(-9,~0\right) $ .	2
1012	Find the difference of the vectors $ \vec{v_1} = \left(-20,~45\right) $ and $ \vec{v_2} = \left(37,~-1\right) $ .	2
1013	Find the difference of the vectors $ \vec{v_1} = \left(-20,~45\right) $ and $ \vec{v_2} = \left(-37,~1\right) $ .	2
1014	Find the difference of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(3,~3 \sqrt{ 3 }\right) $ .	2
1015	Find the projection of the vector $ \vec{v_1} = \left(6,~0\right) $ on the vector $ \vec{v_2} = \left(3,~3 \sqrt{ 3 }\right) $.	2
1016	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-2,~1\right) $ .	2
1017	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 26 }{ 5 },~\dfrac{ 5 }{ 2 },~-\dfrac{ 9 }{ 2 }\right) $ .	2
1018	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(40,~-30\right) $ .	2
1019	Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(5,~7\right) $ .	2
1020	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
1021	Find the difference of the vectors $ \vec{v_1} = \left(6,~9,~3\right) $ and $ \vec{v_2} = \left(1,~3,~0\right) $ .	2
1022	Find the sum of the vectors $ \vec{v_1} = \left(-2,~9\right) $ and $ \vec{v_2} = \left(5,~6\right) $ .	2
1023	Find the difference of the vectors $ \vec{v_1} = \left(-6,~7\right) $ and $ \vec{v_2} = \left(3,~8\right) $ .	2
1024	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-5\right) $ .	2
1025	Find the sum of the vectors $ \vec{v_1} = \left(-4,~-4\right) $ and $ \vec{v_2} = \left(1,~-4\right) $ .	2
1026	Find the difference of the vectors $ \vec{v_1} = \left(-4,~-4\right) $ and $ \vec{v_2} = \left(1,~-4\right) $ .	2
1027	Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~7\right) $ and $ \vec{v_2} = \left(10,~4\right) $ .	2
1028	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-9,~7\right) $ .	2
1029	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(110,~0\right) $ .	2
1030	Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 1 }{ 10 },~\dfrac{ 1 }{ 5 }\right) $.	2
1031	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 81 }{ 1000 },~-\dfrac{ 327 }{ 500 }\right) $ .	2
1032	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~1\right) $ .	2
1033	Find the sum of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ .	2
1034	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~3\right) $ and $ \vec{v_2} = \left(0,~3,~1\right) $ .	2
1035	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(3,~-6\right) $ .	2
1036	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-6,~8\right) $ .	2
1037	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(32,~-24\right) $ .	2
1038	Find the angle between vectors $ \left(3,~4\right)$ and $\left(-8,~7\right)$.	2
1039	Calculate the dot product of the vectors $ \vec{v_1} = \left(1275,~2500\right) $ and $ \vec{v_2} = \left(\dfrac{ 66 }{ 5 },~\dfrac{ 41 }{ 5 }\right) $ .	2
1040	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
1041	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(2,~8\right) $ .	2
1042	Find the angle between vectors $ \left(3,~4\right)$ and $\left(2,~8\right)$.	2
1043	Find the projection of the vector $ \vec{v_1} = \left(3,~4\right) $ on the vector $ \vec{v_2} = \left(2,~8\right) $.	2
1044	Find the sum of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ .	2
1045	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-24\right) $ and $ \vec{v_2} = \left(6,~1\right) $ .	2
1046	Find the angle between vectors $ \left(-2,~1\right)$ and $\left(-1,~-4\right)$.	2
1047	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~5\right) $ .	2
1048	Determine whether the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(-5,~11\right) $ are linearly independent or dependent.	2
1049	Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~-4\right) $ and $ \vec{v_2} = \left(-2,~\dfrac{ 1 }{ 4 }\right) $ .	2
1050	Determine whether the vectors $ \vec{v_1} = \left(-5,~-4\right) $ and $ \vec{v_2} = \left(-2,~\dfrac{ 1 }{ 4 }\right) $ are linearly independent or dependent.	2