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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 zx planes, respectively. If G is the centroid of triangle PQR then area of triangle AOG is (O is the origin)

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a

0

b

a2+b2+c2

c

23(a2+b2+c2)

d

2(a2+b2+c2)

answer is A.

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Detailed Solution

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 OA⇀×OG=ijkabca3b3c3⇀=0

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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 zx planes, respectively. If G is the centroid of triangle PQR then area of triangle AOG is (O is the origin)