Question

The equation of plane passing through the points (2, 2, 1) and (9, 3, 6) and perpendicular to the plane $2 x + 6 y + 6 z = 1$ is

• A. $3 x + 4 y + 5 z = 9$
• B. $3 x + 4 y + 5 z = 0$
• C. $3 x + 4 y - 5 z = 9$
• D. None of these

Answer 1

Answer: (C)

$3 x + 4 y - 5 z = 9$

Answer 2

We know that, equation of plane is

$a \left( x - x _ { 1 } \right) + b \left( y - y _ { 1 } \right) + c \left( z - z _ { 1 } \right) = 0$

It passes through (2, 2, 1)

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

Plane (i) also passes through (9, 3, 6) and is perpendicular to the plane $2 x + 6 y + 6 z = 1$

$\therefore$ $7 a + b + 5 c = 0$ ……(ii)

and $2 a + 6 b + 6 c = 0$ ……(iii)

$\frac { a } { 6 - 30 } = \frac { b } { 10 - 42 } = \frac { c } { 42 - 2 }$ or $\frac { a } { - 24 } = \frac { b } { - 32 } = \frac { c } { 40 }$

or $\frac { a } { 3 } = \frac { b } { 4 } = \frac { c } { - 5 } = k$ (say)

From equation (i), $3 k ( x - 2 ) + 4 k ( y - 2 ) + ( - 5 ) k ( z - 1 ) = 0$

Hence, $3 x + 4 y - 5 z = 9$