- #1
roam
- 1,271
- 12
1. I found the parametric equation of a plane;
[tex]\left(\begin{array}{ccc}x\\y\\z\end{ar ray}\right) =[/tex] [tex]\left(\begin{array}{ccc}1\\2\\3\end{ar ray}\right)[/tex] +s[tex]\left(\begin{array}{ccc}1\\1\\0\end{ar ray}\right)[/tex] +t [tex]\left(\begin{array}{ccc}2\\1\\-1\end{ar ray}\right)[/tex]
s,t ∈ R.
I was asked to find a Cartesian equation. So I write down the three equations;
x=1+s+2t
y=2+s+t
z=3−t
I don't understand how this set can be solved. What's the aim? Do I need to eliminate s,t from the equations?
3. The Attempt at a Solution
1) x=1+s+2t
2) y=2+s+t
3) z=3−t
If I subtract (1) and (2) => x–y=t–1
Subtracting the third from the second => y-z = s-1+2t
And I can also find an expression for t, from the (3) => t=3-z
Could you please show me how we can use this info to find the cartesian equation of the plane.
[tex]\left(\begin{array}{ccc}x\\y\\z\end{ar ray}\right) =[/tex] [tex]\left(\begin{array}{ccc}1\\2\\3\end{ar ray}\right)[/tex] +s[tex]\left(\begin{array}{ccc}1\\1\\0\end{ar ray}\right)[/tex] +t [tex]\left(\begin{array}{ccc}2\\1\\-1\end{ar ray}\right)[/tex]
s,t ∈ R.
I was asked to find a Cartesian equation. So I write down the three equations;
x=1+s+2t
y=2+s+t
z=3−t
I don't understand how this set can be solved. What's the aim? Do I need to eliminate s,t from the equations?
3. The Attempt at a Solution
1) x=1+s+2t
2) y=2+s+t
3) z=3−t
If I subtract (1) and (2) => x–y=t–1
Subtracting the third from the second => y-z = s-1+2t
And I can also find an expression for t, from the (3) => t=3-z
Could you please show me how we can use this info to find the cartesian equation of the plane.