Need help with curve of intersection

Question

I have $16x^2+y^2=16$ and $x+y+z=7$

I need to find the length of the curve of intersection of these two.

This is what I did:

$$\begin{align} &x^2+\frac{y^2}{16}=1\\ &x=\cos t\\ &y = 4\sin t\\ &z = 7-\cos t - \sin t \end{align}$$

so the vector equation is

but it shows that this is not correct, because the plot doesn't work.Please let me know what went wrong.

Answer 1

You should have

$$ z = 7 - x - y = 7 - \cos t - 4 \sin t.$$