The equation of the plane bisecting the line segment joining the points (2,0,6) and (-6,2,4) and perpendicular to it, is

Step-by-step solution

Let variable point on the plane is (x, y, z) . Mid-point of the line segment joining the points (2,0,6) and (-6,2,4)=(-2,1,5) Direction ratio of the line segment joining the points (2,0,6) and (-6,2,4) (-6-2),(2-0),(4-6)-8,2,-2=a₁, b₁, c₁ direction ratios of line joining (x, y, z) and (-2,1,5) =(x+2),(y-1),(z-5)=a₂, b₂, c₂ direction ratio's a₁, b₁, c₁ and a₂, b₂, c₂ are perpendicular so, a₁ a₂+b₁ b₂+c₁ c₂=0 So, required equation of plane is array rrrl & -8(x+2)+2(y-1)-2(z-5) & =0 & -8 x-16+2 y-2-2 z+10 & =0 & -8 x+