Question
Find the equation of a plane through the origin and perpendicular to $x-y+z=5$ and $2 x+y-2 z=7$
Step 1
The normal vector of a plane with equation $ax+by+cz=d$ is given by the vector $\vec{n}=(a,b,c)$. So, for the plane $x-y+z=5$, the normal vector $\vec{n_1}=(1,-1,1)$ and for the plane $2x+y-2z=7$, the normal vector $\vec{n_2}=(2,1,-2)$. Show more…
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