If the centroid of triangle whose vertices are (a, 1,3) , (-2, ~b ,-5) and (4,7, c ) be the origin, then a ^2+ b ^2+ c ^2=

Step-by-step solution

Centroid of triangle with vertices (x₁, y₁, z₁ ), (x₂, y₂ . , .z₂ ) and (x₃, y₃, z₃ ) is ( x₁+x₂+x₃ 3 , y₁+y₂+y₃ 3 , z₁+z₂+z₃ 3 ) For (a, 1,3),(-2, b,-5)(4,7, c) ; if centroid is (0,0,0) 0= a-2+4 3 a=-2 aligned & 0= 1+b+7 3 b=-8 & 0= 3-5+c 3 c=2 aligned aligned & a^2+b^2+c^2 & =(-2)^2+(-8)^2+2^2 & =4+64+4 & =72 aligned