1.

In a three-dimensionalcoordinate 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. noneof these

Answer» Correct Answer - a
Point A is `(a,b,c)implies"Points "P,Q,R" are"(a,b,-c),(-a,b,c)and(a,-b,c)`, respectively
`implies` Centroid of triangle PQR is `((a)/(3),(b)/(3),(c)/(3))`
`implies((a)/(3),(b)/(3),(c)/(3))`
`impliesA,O,G" are"" collinear"`
`implies` Area of triangle AOG is zero.


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