If the foot of the perpendicular from the origin to plane is `P(a ,b ,c)` , the equation of the plane is a. `x/a=y/b=z/c=3` b. `a x+b y+c z=3` c. `a x+b y+c z=a^(2)+b^2+c^2` d. `a x+b y+c z=a+b+c`

If the foot of perpendicular from the point (1,-5,-10) to the plane x-y+z=5 is (a,b,c) then a+b+c=

If x+y+z=0 prove that |a x b y c z c y a z b x b z c x a y|=x y z|a b cc a bb c a|

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

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

From the point P(a,b,c), let perpendicualars PL and PM be drawn to YOZ and ZOX planes,respectively.Then the equation of the plane OLM 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

Evaluate each of the following algebraic expressions for x=1,\ y=-1, z=2,\ a=-2,\ b=1,\ c=-2: (i) a x+b y+c z (ii) a x^2+b y^2-c z^2 (iii) a x y+b y z+c x y

If x ,y ,z are different from zero and "Delta"=|[a, b-y ,c-z],[ a-x, b ,c-z],[ a-x, b-y, c]|=0, then the value of the expression a/x+b/y+c/z is 0 b. -1 c. 1 d. 2