Jun 23, 2016 · $(1,0)$ is a unit vector, but not a basis vector in that case. But you could also consider another basis made of $(0,1)$ and $(1,0)$, then $(1,0)$ would also be a unit vector. A last thing: a unit vector does not "do" anything (if we set dual spaces aside...). But there are operators, such as the inner product, which "do" some things.

Feb 1, 2018 · Since a vector is not characterized with an origin but only with a direction and a magnitude, the point from which it is drawn could be arbitrary. What can be meant by movement though is a change in direction as you quoted. As a side note, a difference is to be made between what he calls unit vectors and position vector. The first only holds a ...

Feb 5, 2020 · A vector space is a space that fulfills the vector axioms, closure under vector addition and scalar multiplication being the ones pertinent to this case. With all of the vector space axioms, any finite dimensional vector space has a basis set such that every vector can be written as a linear combination of the basis vectors.

As ZeroTheHero explained, $\hat{r}$ is a radial unit vector. 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.

Nov 2, 2022 · It represents the instantaneous velocity vector directed along the tangent to the moving path. It is the sum of resolved radial ( same direction as position vector) and ( the perpendicular) circumferential components of velocity. The changes occur whether or not the initial position vector is of unit length or not.

Nov 4, 2016 · Just as OkThen's answer pointed out, the unit vectors can be thought of as derivatives. More precisely, they live in tangent spaces at each point. So to compare the unit vectors at each point, one would need to relate the tangent spaces somehow.

Oct 25, 2016 · $\hat r$ is a unit vector which is pointing from the other charge to the charge itself. The vector version of Coulomb's law is: $$\vec F_1=k\frac{q_1q_2}{r^2}\hat r_{21}$$ Note the difference in notation from your expression: $\vec F_1$ is the force felt by charge 1. $\hat r_{21}$ is the unit vector from charge 2 towards 1.

Mar 8, 2021 · I am then told that both parts of the law can be put into vector form as $$\vec{n}_2 = \vec{n}_1 - 2(\vec{n}_1 \cdot \vec{s}) \vec{s},$$ where $\vec{n}_1$ , $\vec{n}_2$ , and $\vec{s}$ are the unit vectors of the incident ray, the reflected …

Dec 26, 2018 · The choice of unit vectors $\lbrace\hat{i}, \hat{j}, \hat{k}\rbrace$ is part of the process of fixing a reference frame and a set of axis. Since your three unit vectosr are cartesian, then your components will be cartesian components, and they satisfy $$\vec{A}_x=A_x \cdot \hat{i}; \quad \vec{A}_y=A_y \cdot \hat{j};\quad \vec{A}_z=A_z \cdot ...

Oct 14, 2020 · Loosely speaking, you can think of a unit vector to be synonymous to direction or rather a mathematical analogue of the word 'direction'. So we can make the following comment, if you do not change your direction, your unit vector do not change. But if you do change your direction during your motion, the unit vector change changes.