When are unit vectors helpful?

[TbbZz]

When are unit vectors helpful?

It seems to me that it is simply a way to rewrite a given vector component, but with an extra, redundant letter (i, j, k).

Thanks in advance.

 

[Mapes]

Just one example is the unit normal to a surface: a vector (generally with i, j, and k components) perpendicular to a surface, pointing outward by convention. If you want to know the exit flux of a vector field from a region, for example, you just integrate the dot product of the field and the unit normal.

 

[rock.freak667]

When are unit vectors helpful?

It seems to me that it is simply a way to rewrite a given vector component, but with an extra, redundant letter (i, j, k).

Thanks in advance.

When you have forces on an object in the cartesian plane. It makes finding the resultant force about some point easier than taking forces and the angles and using components. Makes torque easier to get with $\vec{r} \times \vec{F}$

 

[TbbZz]

Thanks.

So, in other words, i, j, and k are simply labels given to values of Vx, Vy, and Vz to make it easier to keep track of them (i.e. not adding a Vx to a Vy) during calculations?

 

[rock.freak667]

Thanks.

So, in other words, i, j, and k are simply labels given to values of Vx, Vy, and Vz to make it easier to keep track of them (i.e. not adding a Vx to a Vy) during calculations?

yes, basically you can think of it like that. Instead of dealing with horizontal and the vertical separately , you can do both without being confused.