If the origin is the centroid of the triangle with vertices `P(2a ,\ 2,6),\ Q(-4,3b ,-10)a b n d\ R(8, 14 ,2c)` , find the values of `a\ a n d\ bdot`

Explanation

Given that the triangle with vertices `P(2a ,\ 2,6),\ Q(-4,3b ,-10)a b n d\ R(8, 14 ,2c)`
the origin is the centroid of the triangle .
by using the formula for calculating coordinates of the centroid of the triangle,
the coordinate of centroid of ΔPQR
`=((2a-4+8)/3,(2+3b+14)/3,(6-10+2c)/3)`
`=((2a+4)/3,(3b+16)/3,(2c-4)/3)`
It is given that origin is the centroid of the triangle.
so,`(2a+4)/3=0,(3b+16)/3=0,(2c-4)/3=0`
`=>a=-2,b=-16/3,c=2`
hence the value of `a=-2 and b=-16/3`