Problem 196
Write in scalar form the plane vec r·(vec i-vec j+vec k)=2
Write in scalar form the plane $\vec r\cdot(\vec i-\vec j+\vec k)=2$.
Explanation of Method
Converting a vector equation of a plane into scalar form.
Step 1: Solution
With $\vec r=x\vec i+y\vec j+z\vec k$ and the orthonormality of $\vec i,\vec j,\vec k$: $x-y+z=2,\qquad \vec n=\{1,-1,1\}$.
Result
\[\boxed{\,x-y+z=2,\qquad \vec n=\{1,-1,1\}\,}\]