Show that the planes `ax+by+r=0,by +cz+p=0` and `cz+ax+q=0` are prependicular to `xy,yz and zx` planes respectively.

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.

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.

Show that the plane ax + by + cz + d = 0 divides, the line segment joining the points (x_1, y_1, z_1) and (x_2, y_2, z_2) in the- ratio -(ax_1+by_1+cz_1+d)/(ax_2+by_2+cz_2+d) .

Show that the lines ax+by+c=0, ax-by+c=0, ax-by=c ax+ by-c=0 (a ne b) enclose a rhombus whose area is (2c^(2))/(ab) sq unit.

If the quadrilateral formed by the lines ax + by + c = 0, a'x + b'y + c' = 0, ax + by + c' = 0,a'x + b'y + c = 0 have perpendicular diagonals, then :

From a points P(a,b,c) prependiculars PL,PM and PN are drown to xy,yz and zx planes. Find the equation of the plane passing through L,M and N.

Find the equation of the plane which constant the line of intesection of the planes vecr.( hati+2 hatj+3 hatk)-4=0 and vecr.( 2 hati+ hatj-hatk)=0 and which is prependicular to the plane vecr.(5 hati+3 hatj-6 hatk)+8=0.

The equation of the plane through the line of intersection of the planes ax + by+cz + d= 0 and a'x + b'y+c'z + d'= 0 parallel to the line y=0 and z=0 is

If from a point P(a, b, c), perpendiculars PA and PB are drawn to YZ and ZX-planes respectively, then the equation of the plane OAB is

Show that the plane ax+by+ca+d=0 divides the line joining the points (x_1,y_1,z_1) & (x_2,y_2,z_2) in the ratio - (ax_1+by_1+cz_1+d_1)/(ax_2+by_2+cz_2+d_2)