Vectors – Solved Problems Database

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

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ID	Problem	Count
951	Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right) $ on the vector $ \vec{v_2} = \left(- \dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right) $.	2
952	Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right)$ and $\left(- \dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right)$.	2
953	Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right)$ and $\left(\dfrac{ 683 }{ 1000 },~-\dfrac{ 683 }{ 1000 }\right)$.	2
954	Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 683 }{ 1000 },~-\dfrac{ 683 }{ 1000 }\right) $.	2
955	Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 183 }{ 1000 },~-\dfrac{ 183 }{ 1000 }\right) $ and $ \vec{v_2} = \left(- \dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right) $ .	2
956	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(11.6881,~32.6073\right) $ .	2
957	Find the sum of the vectors $ \vec{v_1} = \left(11.6881,~32.6073\right) $ and $ \vec{v_2} = \left(7.8137,~6.5564\right) $ .	2
958	Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-3\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ .	2
959	Find the projection of the vector $ \vec{v_1} = \left(2,~4\right) $ on the vector $ \vec{v_2} = \left(1,~-1\right) $.	2
960	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~12\right) $ and $ \vec{v_2} = \left(0,~6\right) $ .	2
961	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 88 }{ 5 },~1,~1\right) $ .	2
962	Find the projection of the vector $ \vec{v_1} = \left(-3,~4,~-\sqrt{ 7 }\right) $ on the vector $ \vec{v_2} = \left(3,~-4,~\sqrt{ 7 }\right) $.	2
963	Find the projection of the vector $ \vec{v_1} = \left(3,~-4,~\sqrt{ 7 }\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $.	2
964	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~-4,~\sqrt{ 7 }\right) $ .	2
965	Find the angle between vectors $ \left(\sqrt{ 3 },~-7,~0\right)$ and $\left(\sqrt{ 3 },~1,~-2\right)$.	2
966	Find the sum of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ .	2
967	Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ .	2
968	Find the projection of the vector $ \vec{v_1} = \left(1,~-1,~1\right) $ on the vector $ \vec{v_2} = \left(1,~1,~-2\right) $.	2
969	Find the angle between vectors $ \left(3,~5\right)$ and $\left(5,~3\right)$.	2
970	Determine whether the vectors $ \vec{v_1} = \left(4,~4\right) $ and $ \vec{v_2} = \left(5,~5\right) $ are linearly independent or dependent.	2
971	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~4\right) $ .	2
972	Find the angle between vectors $ \left(4,~5\right)$ and $\left(6,~8\right)$.	2
973	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~5\right) $ .	2
974	Find the difference of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(6,~8\right) $ .	2
975	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(2,~1\right) $ .	2
976	Find the angle between vectors $ \left(3,~-8,~6\right)$ and $\left(-5,~4,~9\right)$.	2
977	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-96,~-57,~-28\right) $ .	2
978	Calculate the cross product of the vectors $ \vec{v_1} = \left(-96,~-57,~-28\right) $ and $ \vec{v_2} = \left(-2,~0,~7\right) $ .	2
979	Find the angle between vectors $ \left(-96,~-57,~-28\right)$ and $\left(-2,~0,~7\right)$.	2
980	Find the sum of the vectors $ \vec{v_1} = \left(9,~4\right) $ and $ \vec{v_2} = \left(1,~7\right) $ .	2
981	Find the angle between vectors $ \left(1,~2,~2\right)$ and $\left(2,~2,~1\right)$.	2
982	Find the angle between vectors $ \left(1,~0,~0\right)$ and $\left(-1,~0,~1\right)$.	2
983	Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(-8,~1,~2\right)$.	2
984	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 9 }{ 2 },~0\right) $ .	2
985	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 9 }{ 2 },~\dfrac{ 16 }{ 5 }\right) $ .	2
986	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 21 }{ 4 },~7\right) $ .	2
987	Find the angle between vectors $ \left(\dfrac{ 21 }{ 4 },~7\right)$ and $\left(3,~4\right)$.	2
988	Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-1\right) $ and $ \vec{v_2} = \left(-7,~-9\right) $ .	2
989	Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(-6,~5\right) $ .	2
990	Find the sum of the vectors $ \vec{v_1} = \left(0,~2,~-3\right) $ and $ \vec{v_2} = \left(2,~6,~4\right) $ .	2
991	Find the sum of the vectors $ \vec{v_1} = \left(8,~6\right) $ and $ \vec{v_2} = \left(-6,~0\right) $ .	2
992	Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~1\right) $ and $ \vec{v_2} = \left(1,~10\right) $ .	2
993	Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~1\right) $ and $ \vec{v_2} = \left(10,~1\right) $ .	2
994	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-4,~1\right) $ .	2
995	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ .	2
996	Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-4\right) $ and $ \vec{v_2} = \left(-8,~-4\right) $ .	2
997	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~6\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ .	2
998	Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~-4\right) $ and $ \vec{v_2} = \left(5,~1\right) $ .	2
999	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~-1\right) $ .	2
1000	Find the projection of the vector $ \vec{v_1} = \left(-7,~-3\right) $ on the vector $ \vec{v_2} = \left(1,~-1\right) $.	2