Question

The equation of the plane passing through the points (3,2,2) and (1,0,–1) and parallel to the line $\frac{x - 1}{2} = \frac{y - 1}{- 2} = \frac{z - 2}{3}$, is

• A. $4x - y - 2z + 6 = 0$
• B. $4x - y + 2z + 6 = 0$
• C. $4x - y - 2z - 6 = 0$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Equation of plane passing through the point (1,0,–1) is,

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

Also, plane (i) is passing through (3, 2, 2)

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

or $2 a + 2 b + 3 c = 0$ …..(i)

Plane (i) is also parallel to the line$\frac { x - 1 } { 2 } = \frac { y - 1 } { - 2 } = \frac { z - 2 } { 3 }$

$\therefore$ $2 a - 2 b + 3 c = 0$ …..(ii)

From (i) and (ii),$\frac { a } { - 3 } = \frac { b } { 0 } = \frac { c } { 2 }$

Therefore, the required plane is,

$- 3 ( x - 1 ) + 0 ( y - 0 ) + 2 ( z + 1 ) = 0$ or $- 3 x + 2 z + 5 = 0$.