Question:

# Sum of operations involving an arbitrary number of 2D vectors

Aubrey: 2 days ago

I need to define an equation stating that the sum of `n` operations involving `n` 2D vectors and `n` scalars yields zero, where `n` is an arbitrary integer greater than 1.

For example, think of it as `Sum[(v_i + t)*(Norm[v_i+t]-L_i), {i, 1, n}] == 0` where `v_i` are the `n` 2D vectors, `t` is the unknown (which is also a 2D vector), and `L_i` are the `n` scalars.

How should I define the `v_i` vectors and the `L_i` scalars so that I can best index them from the sum operator? Note that the `Norm[]` operator is used, so Mathematica needs to know vectors are 2D, and that scalars are scalars (i.e. I just cannot define the equation like if all variables were scalars and understand them as vectors in an abstract way).

Kai: 2 days ago

``````t = {tx, ty}
``````

Assuming you have already defined your `v` and `L` on your own, here I provide some random values for them

## Option 1

``````ClearAll[v, L]
Do[v[i] = RandomReal[1, 2], {i, 7}]
Do[L[i] = RandomReal, {i, 7}]
``````

``````Sum[(v[i] + t)*(Norm[v[i] + t] - L[i]), {i, 1, 7}] == 0
`````` ## Option 2

``````ClearAll[v, L]
v = RandomReal[1, {7, 2}]
L = v = RandomReal[1, {7, 2}]
Sum[(v[[i]] + t)*(Norm[v[[i]] + t] - L[[i]]), {i, 1, 7}] == 0
``````

Notice the difference in the definitions for `v` and `L` use of down values or own values in the two options. See here (https://mathematica.stackexchange.com/q/96/10397).

Is that what you need?