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When reading about vectors I sometimes have seen unit vectors multiplied by the components and other times I've seen basis vectors used instead. Occasionally $$v=x \hat i+y \hat j+z \hat k$$

$$v=xe_x+ye_y+ze_z$$ Occasionally, I've seen both used in a single source. 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).

My questions are: What is the difference between an unit vector and a basis vector? And are they interchangeable in specifying the directions of components?

When reading about vectors I sometimes have seen unit vectors multiplied by the components and other times I've seen basis vectors used instead. Occasionally, I've seen both used in a single source. 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).

My questions are: What is the difference between an unit vector and a basis vector? And are they interchangeable in specifying the directions of components?

When reading about vectors I sometimes have seen unit vectors multiplied by the components and other times I've seen basis vectors used instead. $$v=x \hat i+y \hat j+z \hat k$$

$$v=xe_x+ye_y+ze_z$$ Occasionally, I've seen both used in a single source. 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).

My questions are: What is the difference between an unit vector and a basis vector? And are they interchangeable in specifying the directions of components?

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# Unit Vector vs. Basis Vector

When reading about vectors I sometimes have seen unit vectors multiplied by the components and other times I've seen basis vectors used instead. Occasionally, I've seen both used in a single source. 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).

My questions are: What is the difference between an unit vector and a basis vector? And are they interchangeable in specifying the directions of components?