(Edited to address the follow-up question posted
as a comment to an earlier version of this answer).

Obtain a complete expression using string formatting:

```
sage: x, y, z = SR.var('x y z')
sage: u = vector([0, 1, 1])
sage: uu = vector([1, 2, -1])
sage: v = vector([x, y, z])
sage: print(' + '.join('({})*({})'.format(a, b) for a, b in zip(u, v)))
(0)*(x) + (1)*(y) + (1)*(z)
sage: print(' + '.join('({})*({})'.format(a, b) for a, b in zip(uu, v)))
(1)*(x) + (2)*(y) + (-1)*(z)
```

The parentheses are maybe not so nice but they take
care of keeping things clean whether coefficients are
positive, negative or zero.

If one wants to push the "pretty-printing" effort a little,
one should probably write a function. For example:

```
def axbycz(u):
r"""
Return a custom string for the scalar product of
this vector with the vector (x, y, z), keeping zeros.
EXAMPLES::
sage: axbycz(vector([0, 1, 1]))
'0x + y + z'
sage: axbycz(vector([1, 2, -1]))
'x + 2y - z'
sage: print(axbycz(vector([0, 1, 1])))
0x + y + z
sage: print(axbycz(vector([1, 2, -1])))
x + 2y - z
"""
aa = lambda c: '' if c == 1 else '-' if c == -1 else c
bc = lambda c: '+ {}'.format(aa(c)) if c >=0 else '- {}'.format(aa(-c))
a, b, c = u
return '{}x {}y {}z'.format(aa(a), bc(b), bc(c))
```

where the output will be as in the examples
included in the function's documentation.

One could instead decide to have the function print a result
rather than return a string.

```
def print_axbycz(u):
r"""
Print a custom string for the scalar product of
this vector with the vector (x, y, z), keeping zeros.
EXAMPLES::
sage: print_axbycz(vector([0, 1, 1]))
0x + y + z
sage: print_axbycz(vector([1, 2, -1]))
x + 2y - z
"""
aa = lambda c: '' if c == 1 else '-' if c == -1 else c
bc = lambda c: '+ {}'.format(aa(c)) if c >=0 else '- {}'.format(aa(-c))
a, b, c = u
print('{}x {}y {}z'.format(aa(a), bc(b), bc(c)))
```