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 coordinate system, P ,Q ,a n dR are images of a point A(a ,b ,c) in the x-y ,y-za n dz-x planes, respectively. If G is the centroid of triangle P Q R , then area of triangle A O G 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 coordinate system, P ,Q ,a n dR are images of a point A(a ,b ,c) in the x-y ,y-za n dz-x planes, respectively. If G is the centroid of triangle P Q R , then area of triangle A O G 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

A plane meets the coordinate axes at A, B and C respectively such that the centroid of triangle ABC is (p, q, r). The equation of the plane is

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

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 ?

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^2)/(b c)+(b^2)/(c a)+(c^2)/(a b) ?

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

The coordinates of A ,\ B ,\ C are (6,\ 3),\ (-3,\ 5) and (4,\ -2) respectively and P is any point (x ,\ y) . Show that the ratio of the areas of triangles P B C and A B C is |(x+y-2)/7| .

If tangents P Qa n dP R are drawn from a variable point P to thehyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,(a > b), so that the fourth vertex S of parallelogram P Q S R lies on the circumcircle of triangle P Q R , then the locus of P is x^2+y^2=b^2 (b) x^2+y^2=a^2 x^2+y^2=a^2-b^2 (d) none of these