cwasdqwe said:Do we know if the movement takes place in 2 or in 3 dimensions?
nrqed said:...what is the formula for the magnitude of a vector if we know all its components? You must have seen this somewhere...
cwasdqwe said:To define all its components you must know the dimension... but okay, let's assume [itex]v_{z}=0[/itex]...
The magnitude of a vector is calculated using the Pythagorean theorem, where the square root of the sum of the squares of the vector's components is taken. In other words, the magnitude is equal to the square root of (x^2 + y^2 + z^2), where x, y, and z are the components of the vector in three-dimensional space.
The magnitude of a vector represents its size or length, while the direction of a vector represents its orientation in space. In other words, the magnitude is the quantity of the vector, while the direction is the angle at which the vector is pointing.
No, the magnitude of a vector is always a positive number. It represents the distance or length of the vector, which cannot be negative. However, the components of a vector can be negative, which can affect the direction of the vector.
Vector magnitude is used in physics and engineering to represent physical quantities such as force, velocity, and acceleration. It is also used in calculating the magnitude of electric and magnetic fields, as well as in solving problems involving motion and forces in three-dimensional space.
No, the magnitude of a vector cannot be greater than the sum of its components. The magnitude is calculated using the Pythagorean theorem, which takes into account the sum of the squares of the vector's components. Therefore, the magnitude can never exceed the sum of the components.