Question

The equation of the plane which bisects the line joining the points (–1, 2, 3) and (3, –5, 6) at right angle, is

• A. $4x - 7y - 3z = 8$
• B. $4x + 2y - 3z = 28$
• C. $4x - 7y + 3z = 28$
• D. $4x - 7y - 3z = 28$

Answer 1

Answer: (C)

$4x - 7y + 3z = 28$

Answer 2

According to question,$4 x - 7 y + 3 z = k$ …..(i)

Also, plane (i) passes through $\left( \frac { - 1 + 3 } { 2 } , \frac { 2 - 5 } { 2 } , \frac { 3 + 6 } { 2 } \right)$,

then $4 + \frac { 21 } { 2 } + \frac { 27 } { 2 } = k \Rightarrow k = 28$

Therefore, required equation is $4 x - 7 y + 3 z = 28$.