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.

The perpendicular distance of point P(x,y,z) from XY plane is (x+y).

Find the equation of the plane passing through the intersection of the planes 2x - 3y + z-4 = O and x-y + 2 + 1 = 0 and perpendicular to the plane x + 2y - 3z + 6 = 0.

Find the equation of the plane passing through the intersection of the planes x + 2y + 3z-4 = 0 and 2x + y - Z+ 5 = 0 and perpendicular to the plane 5x + 3y + 6z + 8 = 0.

Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x - y + z = 0.

The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d' are perpendicular to each other, if

Prove that the lines x = py + q, z = ry + s and x = p'y + q', z = r'y + s' are perpendicular if pp' + rr' + 1 = 0.

If the lines x = ay + b ,z = cy + d and x= a'z + b',y = c'z + d'' are perpendicular then ..........

The equation of plane containing the line x/2 = y/3 = z/4 and perpendicular the plane which is containing the lines x/3 = y/4 = z/2 and x/4 = y/2 = z/3 is.....

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 in A, B and C. If the planes throught A, B and C parallel to the planes x=0, y=0 and z=0 intersect in Q, then find the locus of Q.

If x > 0, y > 0, z>0 and x + y + z = 1 then the minimum value of x/(2-x)+y/(2-y)+z/(2-z) is