When I create a rooted vector
and a free vector
and dot product them
it gives me 2.
But if I change v1 to
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.