Find the equation of the plane which bisects the line segment joining the points `A(2,3,4)a n dB(4,5,8)` at right angles.

Explanation

The line segment AB is given by
`(x2​−x1​),(y2​−y1​),(z2​−z1​)`

`=(4−2),(5−3),(8−4)=(2,2,4)=(1,1,2)`

Since the plane bisects that right angle AB

is normal is the plane which is `x=i+j​+2k`

Let C be the midpoint of AB
`(x1​+x2​​)/2,(y1​+y2​​)/2,(z1​+z2​​)/2 `

`=C((2+4)/2​,(3+5)/2​,(4+8)/2​)`

`=C(6/2​,8/2​,(12)/2​)=C(3,4,6)`

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