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 b c a+2x b+2y c+2z x y z|=0

From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to Y O Za n dZ O X planes, respectively. Then the equation of the plane O L M is a. x/a+y/b+z/c=0 b. x/a+y/b-z/c=0 c. x/a-y/b-z/c=0 d. x/a-y/b+z/c=0

From the point P(a ,b ,c), let perpendicualars P La n dP M be drawn to Y O Za n dZ O X planes, respectively. Then the equation of the plane O L M is a. x/a+y/b+z/c=0 b. x/a+y/b-z/c=0 c. x/a-y/b-z/c=0 d. x/a-y/b+z/c=0

Show that the normal to the following planes are perpendicular to each other. x-y+z-2=0\ a n d\ 3x+2y-z+4=0

A point P moves on a plane x/a+y/b+z/c=1. A plane through P and perpendicular to O P meets the coordinate axes at A , Ba n d Cdot If the planes through A ,Ba n dC parallel to the planes x=0,y=0a n dz=0, respectively, intersect at Q , find the locus of Qdot

A point P moves on a plane x/a+y/b+z/c=1. A plane through P and perpendicular to O P meets the coordinate axes at A , Ba n d Cdot If the planes through A ,Ba n dC parallel to the planes x=0,y=0a n dz=0, respectively, intersect at Q , find the locus of Qdot

Show that: |b+c c+a a+b q+r r+p p+q y+z z+x x+y|=2|a b c p q r x y z|

Let image of the line (x-1)/3=(y-3)/5=(z-4)/2 in the plane 2x-y+z+3=0 be Ldot A plane 7x+p y+q z+r=0 is such that it contains the line L and perpendicular to the plane 2x-y+z+3=0 then p=1 (b) q=42 p+q+r=30 (d) p+q+r=0

The planes x=0 and y=0 (A) are parallel (B) are perpendicular to each other (C) interesect in z-axis (D) none of these

If from a point P(a ,b ,c) perpendiculars P Aa n dP B are drawn to Y Za n dZ X-p l a n e s find the vectors equation of the plane O A Bdot