In a three-dimensional coordinate system, `P ,Q` , and `R`are images of a point `A(a ,b ,c)` in the `x-y ,y-z` and `z-x` planes, respectively. If `G` is the centroid of triangle `P Q R ,` then area of triangle `AOG` is (`O` is the origin) (A) `0` (B) `a^2+b^2+c^2` (C) `2/3(a^2+b^2+c^2)` (D) none of these

In a three dimensional co-odinate , P, Q and R are images of a point A(a, b, c) in the xy, yz and zx planes, respectively. If G is the centroid of triangle PQR, then area of triangle AOG is (O is origin)

In a dimensional coodinate a system P, Q and R are image of a point A(a, b, c) in the XY they YZ and the ZX planes respectively. If G is the centroid of triangle PQR then area of Triangle AOG is (O is origin).

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

If the plane (x)/(2)+(y)/(3)+(z)/(4)=1 cuts the coordinate axes in A,B,C, then the area of triangle ABC is

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a)2 (b) 2/3 (c) 1/3 (d) 3

Suppose z_(1), z_(2), z_(3) represent the vertices A, B and C respectively of a Delta ABC with centroid at G. If the mid point of AG is the origin, then

If the centroid of the triangle formed by points P(a,b),Q(b,c) and R(c,a) is at the origin, what is the value of a+b+c?

The normals at three points P,Q,R of the parabola y^(2)=4ax meet in (h,k) The centroid of triangle PQR lies on (A)x=0(B)y=0(C)x=a(D)y=a^(*)

A plane meets the coordinate axes in A,B,C such that eh centroid of triangle ABC is the point (p,q,r). Show that the equation of the plane is (x)/(p)+(y)/(q)+(z)/(r)=3