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
6451	Find the magnitude of the vector $∥ v ∥ = (1, 1, 4)$ .	1
6452	Calculate the cross product of the vectors $v_{1} = (1, 1, 3)$ and $v_{2} = (0, 3, 3)$ .	1
6453	Find the difference of the vectors $v_{1} = (1, 2, 3)$ and $v_{2} = (2, - 1, 5)$ .	1
6454	Find the magnitude of the vector $∥ v ∥ = (3, - 4)$ .	1
6455	Find the projection of the vector $v_{1} = (3, - 4)$ on the vector $v_{2} = (4, 3)$ .	1
6456	Find the sum of the vectors $v_{1} = (- 5, 3)$ and $v_{2} = (4, - 2)$ .	1
6457	Find the magnitude of the vector $∥ v ∥ = (0, 1, 0)$ .	1
6458	Calculate the cross product of the vectors $v_{1} = (0, 0, 25)$ and $v_{2} = (\frac{329}{500}, \frac{6}{25}, 0)$ .	1
6459	Calculate the cross product of the vectors $v_{1} = (0, 0, 25)$ and $v_{2} = (\frac{329}{500}, - \frac{239}{1000}, 0)$ .	1
6460	Calculate the cross product of the vectors $v_{1} = (- 50, 0, 0)$ and $v_{2} = (\frac{329}{500}, - \frac{239}{1000}, 0)$ .	1
6461	Calculate the cross product of the vectors $v_{1} = (- 50, 0, 0)$ and $v_{2} = (0, 0, \frac{239}{20})$ .	1
6462	Calculate the dot product of the vectors $v_{1} = (8, - 2, 1)$ and $v_{2} = (- 2, 1, 0)$ .	1
6463	Find the magnitude of the vector $∥ v ∥ = (8, - 2, 1)$ .	1
6464	Find the magnitude of the vector $∥ v ∥ = (- 1, - 4, 1)$ .	1
6465	Calculate the cross product of the vectors $v_{1} = (8, - 2, 1)$ and $v_{2} = (- 2, 1, 0)$ .	1
6466	Find the magnitude of the vector $∥ v ∥ = (3, 2, 2)$ .	1
6467	Calculate the dot product of the vectors $v_{1} = (3, 2, 2)$ and $v_{2} = (- 1, - 4, 1)$ .	1
6468	Find the angle between vectors $(3, 2, 2)$ and $(- 1, - 4, 1)$ .	1
6469	Calculate the dot product of the vectors $v_{1} = (3, 2, 2)$ and $v_{2} = (- 10, 5, 10)$ .	1
6470	Calculate the dot product of the vectors $v_{1} = (- 1, - 4, 1)$ and $v_{2} = (- 10, 5, 10)$ .	1
6471	Find the magnitude of the vector $∥ v ∥ = (3, - 1, - 2)$ .	1
6472	Find the magnitude of the vector $∥ v ∥ = (1, - 1, - 2)$ .	1
6473	Calculate the dot product of the vectors $v_{1} = (1, - 1, - 2)$ and $v_{2} = (3, - 1, - 2)$ .	1
6474	Calculate the dot product of the vectors $v_{1} = (0, 4, - 2)$ and $v_{2} = (3, - 1, - 2)$ .	1
6475	Calculate the dot product of the vectors $v_{1} = (0, 4, - 2)$ and $v_{2} = (1, - 1, - 2)$ .	1
6476	Find the angle between vectors $(3, - 1, - 2)$ and $(1, - 1, - 2)$ .	1
6477	Find the magnitude of the vector $∥ v ∥ = (3, - 2, 0)$ .	1
6478	Find the magnitude of the vector $∥ v ∥ = (3, - 2, 1)$ .	1
6479	Find the magnitude of the vector $∥ v ∥ = (1, 2, 1)$ .	1
6480	Calculate the dot product of the vectors $v_{1} = (1, 2, 1)$ and $v_{2} = (3, 2, - 1)$ .	1
6481	Calculate the dot product of the vectors $v_{1} = (- 4, - 2, 8)$ and $v_{2} = (3, 2, - 1)$ .	1
6482	Calculate the dot product of the vectors $v_{1} = (- 4, - 2, 8)$ and $v_{2} = (3, - 2, 1)$ .	1
6483	Calculate the dot product of the vectors $v_{1} = (- 4, - 2, 8)$ and $v_{2} = (1, 2, 1)$ .	1
6484	Calculate the dot product of the vectors $v_{1} = (3, - 2, 1)$ and $v_{2} = (1, 2, 1)$ .	1
6485	Find the angle between vectors $(3, - 2, 1)$ and $(1, 2, 1)$ .	1
6486	Find the difference of the vectors $v_{1} = (- 4, 7, - 2)$ and $v_{2} = (6, 1, - 4)$ .	1
6487	Calculate the cross product of the vectors $v_{1} = (- 3, 4, 0)$ and $v_{2} = (0, 3, - 3)$ .	1
6488	Calculate the cross product of the vectors $v_{1} = (0, - 1, 5)$ and $v_{2} = (5, 2, 0)$ .	1
6489	Find the magnitude of the vector $∥ v ∥ = (- 2, 2)$ .	1
6490	Calculate the dot product of the vectors $v_{1} = (4, 45)$ and $v_{2} = (7, 25)$ .	1
6491	Calculate the cross product of the vectors $v_{1} = (- 3, - 3, 0)$ and $v_{2} = (0, - 2, - 3)$ .	1
6492	Calculate the cross product of the vectors $v_{1} = (4, - 2, 3)$ and $v_{2} = (3, - 1, 2)$ .	1
6493	Calculate the cross product of the vectors $v_{1} = (1, 2, 3)$ and $v_{2} = (2, 5, 7)$ .	1
6494	Calculate the dot product of the vectors $v_{1} = (- 2, 1, - 3)$ and $v_{2} = (- 1, - 3, - 5)$ .	1
6495	Determine whether the vectors $v_{1} = (1, 2, 12)$ , $v_{2} = (4, - 7, 6)$ and $v_{3} = (7, 9, 9)$ are linearly independent or dependent.	1
6496	Calculate the cross product of the vectors $v_{1} = (- 2, 5, 3)$ and $v_{2} = (3, - 4, - 2)$ .	1
6497	Calculate the cross product of the vectors $v_{1} = (0, 4, 0)$ and $v_{2} = (- 4, - 3, 0)$ .	1
6498	Find the angle between vectors $(1, 2)$ and $(10, 5)$ .	1
6499	Calculate the dot product of the vectors $v_{1} = (- 3, - 2)$ and $v_{2} = (4, 0)$ .	1
6500	Calculate the dot product of the vectors $v_{1} = (1, 1, 0)$ and $v_{2} = (1, 0, 2)$ .	1