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As far as i can tell, they seen to be doing the same thing, i.e., showing what direction each component is pointing while not changing the numerical value of any of the components (this, at least to me, seems to be what a unit vector does) In spherical coordinates there are also tangential unit vectors $\hat {\theta}$ and $\hat {\phi}$, but you don’t need these to write a purely radial field, such as for a point charge. What is the difference between an unit vector and a basis vector?
2 in many physics textbooks it is given the following definition of unit vector As zerothehero explained, $\hat {r}$ is a radial unit vector A unit vector is every vector whose magnitude is 1 unit
I don't like this definition
On one hand, it is quite common to use a notation for unit vectors (for instance a hat, $\hat {u}$) different to the one used for vectors in general (usually, an arrow, $\vec. I might be missing the obvious, but i can't figure out how the unit vectors in spherical coordinates combine to result in a generic vector In cartesian coordinates, we would have for example $ \\ma. However, this does not prove that i was working with a unit vector, as the answer did not evaluate to one
Therefore unit vectors are dimensionless Indeed, it wouldn't make sense to call a vector with magnitude $1 $ m a unit vector, since it also has a magnitude of $100$ cm This is why, for example, coulomb's law can be written in terms of the radial unit vector $\hat {r}$ without it messing up the units Relation of unit vectors of spherical and cartesian coordinates ask question asked 7 years, 5 months ago modified 7 years, 5 months ago
The unit of the dot product is not really meaningful
It's by definition the length of the projection of the first vector onto the second times the length of the second (or vice versa), which does not straightforwardly correspond to any area Except for this parenthetical remark, this makes sense to me, as the unit vectors in curvilinear coordinates are functions of the coordinates, and their derivatives with respect to the coordinates should be easily related to the other unit vectors in an orthogonal coordinates system. For simplicity, start with $\vec s$ as $\hat z$ Define $\theta_i$ and $\theta_r$ appropriately
What component of the incident vector is unchanged by reflection?
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