Find the linear equation of the plane through the point (2,10,6) ( 2 , 10 , 6 ) and parallel to the plane 𝑥+5𝑦+3𝑧+4=0.

Question

Find the linear equation of the plane through the point  and parallel to the plane 

Answer 1

The parallel planes the share the same normal vector n= < 1,5,3 >

Hence the equation of the plane passing through the point (2,10,6) parallel to the given plane

has equation 1(x-2) +5(y-10) +6(z-6) =0