The product of a vector and the length of a polar coordinate

[catsonmars]

Homework Statement

So I am not sure how to multiply these two (A*R^2) together.

Homework Equations

A=( x^2 + y^2 + z^2 ) (xe + y e + z e )
Where x represents the three vector compones

I also have R^2=x^2+y^2+z^2

The Attempt at a Solution

Is the product of A (x^3e + y^3 e + z^3 e )? If so why is that? I would think because of some vector rule I am not sure of.

 

[LCKurtz]

Homework Statement

So I am not sure how to multiply these two (A*R^2) together.

Homework Equations

A=( x^2 + y^2 + z^2 ) (xe + y e + z e )
Where x represents the three vector compones

I also have R^2=x^2+y^2+z^2

The Attempt at a Solution

Is the product of A (x^3e + y^3 e + z^3 e )? If so why is that? I would think because of some vector rule I am not sure of.

You haven't told us what R is. Also, (xe + y e + z e ) is strange notation. Is e the base of natural logarithms? Or is that supposed to represent a vector $\langle x,y,z\rangle$ and is that $\vec R$? Is $R^2$ supposed to represent $\vec R \cdot \vec R$? It would help greatly if you would define your terms and use standard notation.

 

[catsonmars]

R is just (x^2+y^2+z^2)^1/2 and it isn't a vector.

Let me rewrite A
A=( x^2 + y^2 + z^2 ) (x$\hat{x}$ + y$\hat{y}$ + z$\hat{z}$ )

 

[Mark44]

R is just (x^2+y^2+z^2)^1/2 and it isn't a vector.

Let me rewrite A
A=( x^2 + y^2 + z^2 ) (x$\hat{x}$ + y$\hat{y}$ + z$\hat{z}$ )

x² + y² + z² is just a scalar. What happens when you multiply a vector by a scalar?

Also, are $\hat{x}$, $\hat{y}$, and $\hat{z}$ some random unit vectors? If they are unit vectors in the directions of the x, y, and z axes, they are usually written i, j, and k.