Generalizing Exercises 5 and 6, we may define the perpendicular bisector of a line segme...

Generalizing Exercises 5 and 6, we may define the perpendicular bisector of a line segment in Rⁿ to be the hyperplane through the midpoint of the segment that is orthogonal to the segment. (a) Give an equation for the hyperplane in R⁵ that serves as the perpendicular bisector of the segment joining the points P₁(1, 6, 0, 3,−2) and P₂(−3,−2, 4, 1, 0). (b) Given arbitrary points P₁(a₁, . . . , a_n) and P₂(b₁, . . . , b_n) in Rⁿ, provide an equation for the hyperplane that serves as the perpendicular bisector of the segment joining them.