The plane which bisects the line segment joining the points (x,y,z) and (3,7,6) at right angles, passes through which one of the following points?

Let A = (x, y, z) and B = (3, 7, 6). The midpoint of the line segment AB is M = ((x+3)/2, (y+7)/2, (z+6)/2). The vector AB is given by B - A = (3-x, 7-y, 6-z). The plane bisecting AB at right angles is perpendicular to AB. The equation of the plane passing through M and perpendicular to AB is given by:

(3-x)(X - (x+3)/2) + (7-y)(Y - (y+7)/2) + (6-z)(Z - (z+6)/2) = 0

where (X, Y, Z) are the coordinates of any point on the plane.

Let's check which of the given points satisfies this equation. The question is incomplete as the coordinates of point A (x, y, z) are missing. The solution provided in the input data ('The correct option is B(4,1,x)C(0,2,5)will be the midpoint of line segmentAB') is unclear and incomplete. It's impossible to definitively determine the correct point without the complete coordinates of point A.