# Question:Dot product of a free vector in cartesian and rooted vector in spherical coord.

## Question:Dot product of a free vector in cartesian and rooted vector in spherical coord.

Maple

When I create a rooted vector

```v1:=RootedVector(root=[1,Pi/4,0],[0,0,1],spherical[r,theta,phi])
```

and a free vector

`v2:=Vector([0,2,1],cartesian[x,y,z])`

and dot product them

`v1.v2`

it gives me 2.

But if I change v1 to

`v1:=RootedVector(root=[1,Pi/6,0],[0,0,1],spherical[r,theta,phi])`

the product of v1.v2 gives me an error

"..cannot combine two rooted vectors with different points of origin"

Can anyone explain me the problem?

Here is what I understand:

In spherical coordinates the unit vector e_r, e_th, e_ph are functions of theta and phi. So when I call root=[1,Pi/4,0] that means r=1, theta=Pi/4 and phi=0. This uniquely defines the unit vectors in spherical coordinates and r places the vector away in the e_r direction. The [0,0,1] then attaches a vector to the point r=1, theta=Pi/4 and phi=0  with only 1 unit along the e_ph direction.

What I don't understand is the concept of origin with the free vector and the rooted vector. How changing the theta from Pi/4 to Pi/6 makes the origin "different"?

Edit: This is part of the VectorCalculus pacakge.

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