Question

The equation of a plane passing through (1, 2, –3), (0, 0, 0) and perpendicular to the plane 3x – 5y + 2z = 11, is :

• A. $3x+y+\frac{5}{3}z=0$
• B. 4x + y + 2z = 0
• C. $3x-y+\frac{z}{3}=0$
• D. x + y + z = 0

Answer 1

The correct option is D x + y + z = 0

Equation of plane through (0, 0, 0) is
ax + by + cz = 0 . . . .(1)
(1) passes through (1, 2, –3) and ⊥ to the plane
3x – 5y + 2z = 11
$\therefore$ a + 2b – 3c = 0 . . . .(2)
$\therefore$ 3a – 5b + 2c = 0 . . . .(3)
$\Rightarrow \frac{a}{-11}=\frac{b}{-11}=\frac{c}{-11}$
$\Rightarrow a=b=c$
Hence, equation of required plane is x + y + z = 0.