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Q.

In a three dimensional co-ordinate system P,Q,R are images of a point A(2,3,5) in xy,
the yz and zx planes respectively. If G is the centroid of triangle PQR then area of
triangle AOG is _____(O is origin)

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a

38

b

0

c

76

d

30

answer is B.

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Detailed Solution

detailed_solution_thumbnail

Image of (2,3,5) in xy plane = (2,3,-5)
in yz plane =(-2,3,5)
and yz plane= (2,-3,5)
$G = (\frac{2}{3}, \frac{3}{3}, \frac{5}{3})$
Area of $ΔAOG = \frac{1}{2} | AO \times OG |$
$= \frac{1}{2} |\begin{array}{ccc} i & j & k \\ 2 & 3 & 5 \\ \frac{2}{3} & \frac{3}{3} & \frac{5}{3} \end{array}| = 0$

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In a three dimensional co-ordinate system P,Q,R are images of a point A(2,3,5) in xy,the yz and zx planes respectively. If G is the centroid of triangle PQR then area oftriangle AOG is _____(O is origin)