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)

- 0
- a2+b2+c2
- 23(a2+b2+c2)
- 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

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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