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Question

In a three dimensional co - ordinate system P, Q and R are images of a point A(a, b, c) in the xy the yz and the zx planes respectively. If G is the centroid of triangle PQR then area of triangle AOG is (O is the origin)
  1. 0
  2. a2+b2+c2
  3. 23(a2+b2+c2)
  4. 12(a2+b2+c2)


Solution

The correct option is A 0
Point A is (a, b, c)
Points P, Q, R are (a, b, –c), (-a, b, c) and (a, –b, c) respectively.
 centroid of triangle PQR is (a3,b3,c3) G(a3.b3,c3)
 A, O, G are collinear  area of triangle AOG is zero.    The equation of that line is  xa=yb=zc                        

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