Show that `a x+b y+r=0,b y+c z+p=0a n dc z+a x+q=0` are perpendicular to `x-y ,y-za n dz-x` planes, respectively.

In a three-dimensional coordinate system, P ,Q ,a n dR are images of a point A(a ,b ,c) in the x-y ,y-za n dz-x planes, respectively. If G is the centroid of triangle P Q R , then area of triangle A O G is ( O is the origin) a. 0 b. a^2+b^2+c^2 c. 2/3(a^2+b^2+c^2) d. none of these

Show that the lines : 3x-2y+5=0, y+3z-15=0 and (x-1)/5=(y+5)/-3=z/1 are perpendicular to each other.

Show that the equation of the plane through the line x/l=y/m=z/n and perpendicular to the plane containing non perpendicular lines x/m=y/n=z/l and x/n=y/l=z/m is (m-n)x+(-l)y+(l-m)z=0 .

Does the line x=y=0 lie in the plane z=0.

Find the equation of the plane through the line of intersection of the planes 2x+3y-3z+1=0 and x+y-2z+3=0 and perpendicular to the plane 3x-y-2z-4=0 .

A point P moves on a plane (x)/(a)+(y)/(b)+(z)/(c)=1. A plane through P and perpendicular to OP meets the coordinate axes at A, B and C.If the parallel to the planes x=0,y=0 and z=0, respectively, intersect at Q, find the locus of Q.

Find the equation of the plane through the line of intersection of the planes: x+3y-z+1=0 and x+y-2z+3=0 and perpendicular to the plane 3x-y-2z-4=0

P is a point (a, b, c). Let A, B, C be images of P in y-z, z-x and x-y planes respectively, then the equation of the plane ABC is

Find the equation of the plane passing through the line of intersection of the planes 2x-y=0 and 3z-y=0 and perpendicular to the plane 4x+5y-3z=8