UPSC NDA I 2014 Mathematics Paper

Given: Equation of plane 2x+3y−z=7
Now, by comparing the given equation of plane with the standard equation of plane ax+by+cz+d= 0 , we get a=2,b=3,c=−1 and d=−7.
As we know that, for any plane ax+by+cz+d=0 the direction ratios of the normal to the plane are <a,b,c> or <a×k,b×k,c×k> where k∈R.
Hence, the direction ratios of the normal to the given plane are: ⟨2,3,−1⟩