HI fantiniFantini said:The vector itself is responsible for the direction. All you need to do is divide the vector by its magnitude:
$$\vec{u} = \frac{\vec{A}}{\| \vec{A}\|} = \frac{2 \vec{a}_{\rho} - z \vec{a}_z}{\sqrt{4+z^2}}.$$
Fantini said:Yes, it is valid. This is because cylindrical coordinates form an ortonormal system. Thus the length of the vector does not change from cartesian. You can compute the length as you would normally. :)
Drain Brain said:does this also holds for spherical form?
A unit vector is a vector that has a magnitude of 1 and points in a specific direction. In finding a unit vector along $\vec{A}$, it is important because it helps to normalize the given vector, making calculations easier and providing important information about the direction of the vector.
To find the unit vector along $\vec{A}$, you first need to calculate the magnitude of $\vec{A}$. Then, divide $\vec{A}$ by its magnitude to get the unit vector. The formula is $\vec{A}_{unit} = \frac{\vec{A}}{|\vec{A}|}$.
No, a unit vector always has a magnitude of 1, which is a positive number. This is because the purpose of a unit vector is to represent direction, not magnitude.
A unit vector has a magnitude of 1 and represents only direction, while a normal vector can have any magnitude and represents both magnitude and direction.
Unit vectors are commonly used in mathematics and science because they simplify calculations and provide important information about the direction of a vector. They also allow for easier comparison and manipulation of vectors in equations and formulas.