Question

Find the equation of the plane that is parallel to the plane 5x-4y+z=1 and passes through the point (2,-1,-2)

Answer 1

if u replace (x,y,z)=(2,-1,-2) then
\[ \large 5x-4y+z=5\cdot2-4(-1)+(-2)=10+4-2=12 \]
then the planes's equation is
\[ \large 5x-4y+z=12 \]

Answer 2

fundamental point to remeber here is PARALLEL PLANES HAVE SAME NORMALS

So given a plane , find its normal, then use the point normal formula to find the equation of other plane

Answer 3

does that make sense?

Answer 4

Yes, psi9epsilon, thank you!