## plotting – If the level set of real valued function f(x,y,z) is a curve then will ContourPlot3D fail to plot points?

I have the function $$f(x,y,z)=frac{x^2}{2}+x y+frac{y^2}{2}+z^2$$. The solution set to the equation $$f(x,y,z)=0$$ is the line parametrized as $$(t,-t,0)$$. When I use ContourPlot3D on f=0 I get an empty graph. I begin to suspect that ContourPlot3D only works for level sets that are surfaces. Is this correct?

## functions – Replacing \$x,y\$ in \$f(x,y,z)\$ with values from a list

I’m sure there is a simple solution to this using map or apply, but its not occurring to me.

Suppose I have a function $$f(x,y,z)= x+y+z)$$

And I want to evaluate $$f(x,y,1)$$ for $${x,y} ∈ {{1,2},{3,4}}$$

What is the best way to do this?

Examples:

If I use
`f(x_,y_,z_):= x+y+z; f(#1,#2,1)&/@ {{1,2},{3,4}}`

this will give me things like `{{2+#2,3+#2}}.`

On the other hand, `Apply` works on a single element
`f(#1,#2,1)& @@ {1,2}`
but not on a list such as `{{1,2},{3,4}}`. On the list it gives me `{f(1,3,1),f(2,4,1)`

I am not sure how to go from the case of a single pair to a list of pairs