The incenter and centroid of the triangle, whose vertices are A (0,3,0), B (0,0,4) , and C (0,3,4) , are respectively given by

Step-by-step solution

A (0,3,0), B (0,0,4) , and C (0,3,4)a=B C=3b=C A=4c=A B=5 . aligned & Now, Incentre ( a x₁+b x₂+c x₃ a+b+c , a y₁+b y₂+c y₃ a+b+c , a z₁+b z₂+c z₃ a+b+c ) & ( 3 0+4 0+5 0 3+4+5 , 3 3+4 0+5 3 3+4+5 , 3 0+4 4+5 4 3+4+5 ) & (0,2,3) & and centroid ( x₁+x₂+x₃ 3 , y₁+y₂+y₃ 3 , z₁+z₂+z₃ 3 ) aligned aligned & ( 0+0+0 3 , 3+0+3 3 , 0+4+4 3 ) & (0,2, 8 3 ) aligned