# Unit vector notation, why use 3 letters for a component?

Homework Statement:
I understand basic components of a vector in the x and y directions. I can also understand replacing the x with i, and replacing y with j. What I do not understand is why I would use them together as Vxi + Vyj. This seems redundant. Could someone help explain why or when using triple letters would be better than using two ?
Relevant Equations:
V= Vxi + Vyj.
.

## Answers and Replies

hutchphd
Science Advisor
Homework Helper
The term vxi is not redundant. It is not the same as vx alone nor i alone. It describes a vector in a known direction (the x direction) of a particular size. The fact that we choose to label the variable with x is for convenience. While in that equation it may seem redundant, we may wish to write it down sometimes not next to i .
For instance what if I ask for the magnitude of the vector
V= Vxi + Vyj
During the calculation the init vectors go away and yet the label remains.

SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
Homework Statement: I understand basic components of a vector in the x and y directions. I can also understand replacing the x with i, and replacing y with j. What I do not understand is why I would use them together as Vxi + Vyj. This seems redundant. Could someone help explain why or when using triple letters would be better than using two ?
Homework Equations: V= Vxi + Vyj.
.
For one thing, some of those symbols are typically subscripts, for a 2nd thing, some of those symbols will usually be type set in boldface (or written with a harpoon or caret hovering above) to indicate their vector nature. I'll use boldface type for most of the following.

V = Vx + Vy : Here Vx and Vy are component vectors of vector V.

V= Vx i + Vy j : Here Vx and Vy are the components (as scalars) of vector V in the x and y directions respectively. The i and j are each unit vectors in the x and y directions respectively.

Notice that textbooks often denote a unit vector with a caret above as in the following.

##\displaystyle \vec {~V} = V_{x~}\!\hat{\imath} + V_{y~}\!\hat{\jmath} ##​

Added in Edit :
Oh! Sorry I didn't notice, but Last edited: