The plane which bisects the line

Question:

The plane which bisects the line joining the points $(4,-2,3)$ and $(2,4,-1)$ at right angles also passes through the point:

  1.  $(4,0,1)$

  2. $(0,-1,1)$

  3. $(4,0,-1)$

  4. $(0,1,-1)$


Correct Option: , 3

Solution:

Direction ratios of normal to the plane are $<1,-3,2>$.

Plane passes through $(3,1,1)$.

Equation of plane is,

$1(x-3)-3(y-1)+2(z-1)=0$

$\Rightarrow x-3 y+2 z-2=0$

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