Linear Algebra Plane Question

[robbie]

The plane that passes through the point (−3,−5,2) and is perpendicular to both x+4z=0 and 5z−(4x+5y)=−7 has as its implicit equation.

How would you solve this? This is Linear Algebra I think.

 

[pka]

The plane that passes through the point (−3,−5,2) and is perpendicular to both x+4z=0 and 5z−(4x+5y)=−7 has as its implicit equation.

Rewrite \(\displaystyle 5z-(4x+5y)=-7\) as \(\displaystyle 4x+5y-5z=7\). The norma is \(\displaystyle <1,0,4>\times <4,5,-5>\).
See here,