# vector constants and vector functions

I'm using sage (through cocalc) with my multivariable calculus class this year. I'm looking for a consistent way to define symbol vector-valued functions and vector constants.

I can define a symbolic vector-valued function like this:

```
var('t')
r(t) = [1, t]
r(1) + r(2) # works as expected
```

I can define constant vectors like this:

```
a = vector([1, 1])
b = vector([10, 20])
c = a + b # works as expected
```

But `vector`

does not work for symbolic functions: `r(t)=vector([1, t])`

throws.

So:

`vector`

seems**required**for constants, else we don't get correct algebraic behavior`vector`

**cannot**be used with symbolic functions, else sage throws

**Question**: I'm worried this is going to cause a lot of confusion for my students. Is there a consistent way to define vectors for both constant values and symbolic expressions?