JEE Main20203 Sep 2020Evening ShiftMathematicsThree Dimensional GeometryActual

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

Options

A0 ,   − 1 ,   1
B4 ,   0 ,   - 1
C4 ,   0 ,   1
D( 0 ,   1 ,   – 1 )

Correct answer

B. 4 ,   0 ,   - 1

Step-by-step solution

Mid point P ≡ 3 ,   1 ,   1 Normal of plane is along the line A B . Direction ratio's of normal is < 4 - 2 ,   - 2   - 4 ,   3 - - 1 > = < 2 ,   - 6 ,   4 > = < 1 ,   - 3 ,   2 > Equation of plane is 1 x - 3 - 3 y - 1 + 2 z - 1 = 0 ⇒ x - 3 y + 2 z - 2 = 0 Only option B satisfies and is the answer.

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