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
6501	Calculate the dot product of the vectors $v_{1} = (5, - 12)$ and $v_{2} = (15, 8)$ .	1
6502	Calculate the cross product of the vectors $v_{1} = (1, 1, 0)$ and $v_{2} = (1, 0, 2)$ .	1
6503	Find the difference of the vectors $v_{1} = (5, - 12)$ and $v_{2} = (15, 8)$ .	1
6504	Find the projection of the vector $v_{1} = (7, 0)$ on the vector $v_{2} = (9, 0)$ .	1
6505	Find the difference of the vectors $v_{1} = (- 2, - 4, 3)$ and $v_{2} = (3, - 1, - 2)$ .	1
6506	Calculate the dot product of the vectors $v_{1} = (6, - 6)$ and $v_{2} = (4, 5)$ .	1
6507	Find the projection of the vector $v_{1} = (4, - 5)$ on the vector $v_{2} = (3, - 1)$ .	1
6508	Find the angle between vectors $(4, 3)$ and $(- 1, 5)$ .	1
6509	Find the magnitude of the vector $∥ v ∥ = (0, 0)$ .	1
6510	Find the projection of the vector $v_{1} = (5, - 4, - 5)$ on the vector $v_{2} = (2, - 1, 5)$ .	1
6511	Find the projection of the vector $v_{1} = (2, - 1, 5)$ on the vector $v_{2} = (5, - 4, - 5)$ .	1
6512	Determine whether the vectors $v_{1} = (15, - 8)$ and $v_{2} = (- 5, 12)$ are linearly independent or dependent.	1
6513	Calculate the dot product of the vectors $v_{1} = (15, - 8)$ and $v_{2} = (- 5, 12)$ .	1
6514	Find the angle between vectors $(15, - 8)$ and $(- 5, 12)$ .	1
6515	Find the sum of the vectors $v_{1} = (3, - 1)$ and $v_{2} = (12, 15)$ .	1
6516	Find the difference of the vectors $v_{1} = (3, - 1)$ and $v_{2} = (12, 15)$ .	1
6517	Find the angle between vectors $(5, 5)$ and $(- 8, 8)$ .	1
6518	Find the difference of the vectors $v_{1} = (2, 4)$ and $v_{2} = (4, 3)$ .	1
6519	Calculate the dot product of the vectors $v_{1} = (5, 3)$ and $v_{2} = (3, - 5)$ .	1
6520	Find the magnitude of the vector $∥ v ∥ = (2, 1)$ .	1
6521	Calculate the cross product of the vectors $v_{1} = (- 2, - 3, 0)$ and $v_{2} = (4, - 1, 0)$ .	1
6522	Find the magnitude of the vector $∥ v ∥ = (0, 2, - 5)$ .	1
6523	Find the magnitude of the vector $∥ v ∥ = (0, 6)$ .	1
6524	Calculate the dot product of the vectors $v_{1} = (1, 2)$ and $v_{2} = (- 1, 1)$ .	1
6525	Determine whether the vectors $v_{1} = (2, 1, 2)$ , $v_{2} = (1, 2, 1)$ and $v_{3} = (0, 1, 1)$ are linearly independent or dependent.	1
6526	Find the magnitude of the vector $∥ v ∥ = (1, 2, 2)$ .	1
6527	Calculate the cross product of the vectors $v_{1} = (1, 2, - 1)$ and $v_{2} = (2, 1, 4)$ .	1
6528	Calculate the cross product of the vectors $v_{1} = (- 1, 0, 3)$ and $v_{2} = (1, 2, - 1)$ .	1
6529	Calculate the dot product of the vectors $v_{1} = (3, - 1, 4)$ and $v_{2} = (0, 3, - 1)$ .	1
6530	Find the difference of the vectors $v_{1} = (1, 2, 3)$ and $v_{2} = (1, - 1, 4)$ .	1
6531	Calculate the dot product of the vectors $v_{1} = (4, 2)$ and $v_{2} = (2, 4)$ .	1
6532	Find the difference of the vectors $v_{1} = (4, 2)$ and $v_{2} = (2, 4)$ .	1
6533	Calculate the cross product of the vectors $v_{1} = (- 2, 3, 1)$ and $v_{2} = (- 2, 5, 0)$ .	1
6534	Calculate the dot product of the vectors $v_{1} = (2, 3, - 1)$ and $v_{2} = (- 3, 0, 0)$ .	1
6535	Find the magnitude of the vector $∥ v ∥ = (6, - 2)$ .	1
6536	Find the sum of the vectors $v_{1} = (4, - 7)$ and $v_{2} = (5, 1)$ .	1
6537	Find the angle between vectors $(- 1, 3)$ and $(5, 5)$ .	1
6538	Find the magnitude of the vector $∥ v ∥ = (9, - 9)$ .	1
6539	Find the magnitude of the vector $∥ v ∥ = (4, - 8)$ .	1
6540	Find the difference of the vectors $v_{1} = (- 2, 3, - 1)$ and $v_{2} = (2, 1, 3)$ .	1
6541	Find the difference of the vectors $v_{1} = (1, - 2)$ and $v_{2} = (5, - 4)$ .	1
6542	Find the magnitude of the vector $∥ v ∥ = (4, - 7)$ .	1
6543	Calculate the dot product of the vectors $v_{1} = (- 2, - 1)$ and $v_{2} = (2, 1)$ .	1
6544	Calculate the dot product of the vectors $v_{1} = (\frac{3}{10}, - \frac{2}{5}, 0)$ and $v_{2} = (0, 0, \frac{1}{10})$ .	1
6545	Find the magnitude of the vector $∥ v ∥ = (0, 0, 0)$ .	1
6546	Calculate the cross product of the vectors $v_{1} = (\frac{3}{10}, - \frac{2}{5}, 0)$ and $v_{2} = (0, 0, \frac{1}{10})$ .	1
6547	Determine whether the vectors $v_{1} = (1, 4, - 2)$ , $v_{2} = (6, - 2, 8)$ and $v_{3} = (0, 0, 0)$ are linearly independent or dependent.	1
6548	Calculate the dot product of the vectors $v_{1} = (5, 5)$ and $v_{2} = (- 6, 1)$ .	1
6549	Find the sum of the vectors $v_{1} = (- 7, 1)$ and $v_{2} = (- 5, 8)$ .	1
6550	Calculate the cross product of the vectors $v_{1} = (1, - 1, 1)$ and $v_{2} = (3, 4, 2)$ .	1