Physics, Chemistry, Mathematics Forums

Hey Chandni you should be knowing that the intercept form of a plane is (x/a)+(y/b)+(z/c)=1. if you need a proof, see that the points (a,0,0);(0,b,0);(0,0,c) satisfy the equation and a smart girl like you should be knowing that i can have only 1 plane passing through three non-collinear points. So, the point of intersection of the planes x=a;y=b;z=c is obviously (a,b,c) and now you know that the equation for the distance of a point from a plane is same as what we had studied in 2-D.

So distance from the origin is.

[mod(0+0+0-1)]/sqrt[(1/a²)+(1/b²)+(1/c²)]=p

as the required locus is that of (a,b,c), replace (a,b,c) with (x,y,z) you see that you have the answer

            Manoj