An overloaded version of Plus that deals with adding Vectors
v1 + v2
Vector(algebraic); the first Vector to add
Vector(algebraic); the second Vector to add
Returns the sum of the two Vectors.
The following table describes the interaction between different types of Vector objects in different coordinate systems when the overloaded Plus operator is applied.
rooted Vector (root2)
rooted Vector (root1)
rooted Vector (any)
Free Vectors can only be added if they are in cartesian coordinates.
A cartesian free Vector can be added with a rooted Vector
v1 ≔ RootedVector⁡root=1,Pi,1,1,polarr,t
Rooted Vectors can be added if they are in the same coordinate system and are rooted at the same point.
v1 ≔ RootedVector⁡root=1,Pi2,1,2,polarr,t
v2 ≔ RootedVector⁡root=1,Pi2,1,0,polarr,t
When a vector field and a rooted Vector are added, the vector field is evaluated at the root point of the vector and the operation is carried through. The coordinate system of the sum and the vector field are the same.
v3 ≔ RootedVector⁡root=1,Pi3,Pi4,0,1,0,sphericalr,p,t
vf ≔ VectorField⁡y,x,z,cartesianx,y,z
Vector Fields can be added if they are in the same coordinate system.
vf2 ≔ VectorField⁡r,t+Pi,polarr,t
vf3 ≔ VectorField⁡r,t−Pi2,polarr,t
Position Vectors can also be added, the result is a position Vector.
pv1 ≔ PositionVector⁡p,p,polarr,t
pv2 ≔ PositionVector⁡p,p2,cartesianx,y
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