UPSC 2018 Maths Optional Paper 1 Q4d — Step-by-Step Solution

12 marks · Section A

Plane · Analytic Geometry · asked 5× in 13 yrs · Read the full method →

Question

Find the equation of the plane parallel to $3x-y+3z=8$ and passing through the point $(1,1,1)$ .

Parallel planes keep the normal; only the constant changes — fix it from the given point.

Planes parallel to $3x-y+3z=8$ have the same normal $\vec n=(3,-1,3)$ , hence the form

3x-y+3z=k

for some constant $k$ (any value $k\neq8$ gives a distinct parallel plane).

3(1)-(1)+3(1)=3-1+3=5\ \Rightarrow\ k=5.

\boxed{\;3x-y+3z=5.\;}