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 ax+by+r=0,by+cz+p=0 and cz+ax+q=0 are perpendicular to x-y,y-z and z-x planes, respectively.

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

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

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 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 .

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