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

[lboulden]

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.

.

 

[hutchphd]

The term v_xi is not redundant. It is not the same as v_x 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= V_xi + V_yj
During the calculation the init vectors go away and yet the label remains.

 

[SammyS]

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 2^nd 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 = V_x + V_y : Here V_x and V_y are component vectors of vector V.

V= V_x i + V_y j : Here V_x and V_y 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