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