Question

The equation of the plane passing through the point (–1, 3, 2) and perpendicular to each of the planes $x + 2 y + 3 z = 5$ and $3 x + 3 y + z = 0$, is

• A. $7 x - 8 y + 3 z - 25 = 0$
• B. $7 x - 8 y + 3 z + 25 = 0$
• C. $- 7 x + 8 y - 3 z + 5 = 0$
• D. $7 x - 8 y - 3 z + 5 = 0$

Answer 1

Answer: (A)

$7 x - 8 y + 3 z - 25 = 0$

Answer 2

Given, equaiton of plane is passing through the point

(–1, 3, 2)

$\therefore$ $A ( x + 1 ) + B ( y - 3 ) + C ( z - 2 ) = 0$ .....(i)

Since plane (i) is perpendicular to each of the planes $x + 2 y + 3 z = 5$ and $3 x + 3 y + z = 0$

So, $A + 2 B + 3 C = 0$ and $3 A + 3 B + C = 0$

$\therefore$ $\frac { A } { 2 - 9 } = \frac { B } { 9 - 1 } = \frac { C } { 3 - 6 } = K$ ⇒ $A = - 7 K , B = 8 K , C = - 3 K$

Put the values of A, B and C in (i)

we get, $7 x - 8 y + 3 z + 25 = 0$, which is the required equation of the plane.