Problem 266
Write the plane through M_1(2,0,-1) perpendicular to…
Write the plane through $M_1(2,0,-1)$ perpendicular to $2x-y-3=0$ and $x+y-z+1=0$.
Explanation of Method
The plane through M₁(2, 0, −1) perpendicular to two given planes.
Step 1: Solution
\[ \vec n=\{2,-1,0\}\times\{1,1,-1\}=\{1,2,3\}. \]
\[x+2y+3z+1=0\]
Check: $M_1$ gives $2-3+1=0$; $\vec n\cdot\vec n_1=0$; $\vec n\cdot\vec n_2=1+2-3=0$.
Result
\[\boxed{\,x+2y+3z+1=0\,}\]