Question

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

• A. $3x - 4y + 18z + 32 = 0$
• B. $3x + 4y - 18z + 32 = 0$
• C. $4x + 3y - 17z + 31 = 0$
• D. $4x - 3y + z + 1 = 0$

Answer 1

Answer: (D)

$4x - 3y + z + 1 = 0$

Answer 2

Equation of any plane passing through (0, 1, 2) is

$a ( x - 0 ) + b ( y - 1 ) + c ( z - 2 ) = 0$ ......(i)

Plane (i) passes through (–1, 0, 3), then

$a ( - 1 - 0 ) + b ( 0 - 1 ) + c ( 3 - 2 ) = 0$

⇒ $- a - b + c = 0$⇒ $a + b - c = 0$ .....(ii)

Plane (i) is perpendicular to the plane $2 x + 3 y + z = 5$, then $2 a + 3 b + c = 0$ ......(iii)

Solving (ii) and (iii), we get $a = - 4 k , b = 3 k , c = - k$

Putting these values in (i),

$- 4 k ( x ) + 3 k ( y - 1 ) - k ( z - 2 ) = 0$

⇒ $- 4 x + 3 y - 3 - z + 2 = 0$

⇒ $- 4 x + 3 y - z - 1 = 0$ ⇒ $4 x - 3 y + z + 1 = 0$ .