The equation of the plane which bisect the join of point $(7, 2, 3)$ and $(- 1, - 4, 3)$ perpendicularly is

x + 2 y + 3 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 x - y + 3 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x + y + 2 z + 7 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 x + 3 y = 9

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $4 x + 3 y = 9$
Lets assume $P = (7, 2, 3)$ and $Q = (- 1, - 4, 3)$
So mid point of $P Q$ is $(3, - 1, 3) = M$ (say), since plane bisect $P Q$ so $M$ will lie in required plane.
Also direction ratios of $P Q$ are $8, 6, 0$ .
Also given $P Q$ is perpendicular to the plane, thus equation of plane is given by,
$8 (x - 3) + 6 (y + 1) + 0 (z - 3) = 0$
$\Rightarrow 4 x + 3 y - 9 = 0$

Suggest Corrections

Similar questions

Q. The equation of plane containing intersecting lines

\frac{x + 3}{3} = \frac{y}{1} = \frac{z - 2}{2}

and

\frac{x - 3}{4} = \frac{y - 2}{2} = \frac{z - 6}{3}

is _______

Q. Equation of the plane bisecting the angle between the planes

2 x - y + 2 z + 3 = 0

and

3 x - 2 y + 6 z + 8 = 0

Which of the following pairs of linear equations is inconsistent?
$1. x + 3 y - 5 = 0, 2 x + y = 0$
$2. 2 x + y = 1, 2 y = 2 - 4 x$
$3. 2 x - y = 2, 2 y - 4 x = 2$

Q. Equation of a plane bisecting the angle between the planes 2x - y + 2z + 3 = 0 and 3x - 2y + 6z + 8 = 0 is

Q. Find the equation of plane passing through the intersection of the planes

2 x + 3 y - z + 1 = 0

and

x + y - 2 z + 3 = 0

and perpendicular to the plane

3 x - y - 2 z - 4 = 0

Join BYJU'S Learning Program

The equation of the plane which bisect the join of point (7,2,3) and (−1,−4,3) perpendicularly is

The equation of the plane which bisect the join of point $(7, 2, 3)$ and $(- 1, - 4, 3)$ perpendicularly is