Question

Equation of the plane through the point (1, 0, –2) and perpendicular to the planes 2x + y – z – 2 = 0 and x – y –z – 3 = 0 is given by :

• A. 6x – y + 3z = 0
• B. 2x – y + 3z + 4 = 0
• C. 2x + y – z + 4 = 0
• D. 5x + y – z + 4 = 0

Answer 1

The correct option is B 2x – y + 3z + 4 = 0

Equation of the plane through (1, 0, – 2) is
a(x – 1) + by + c(z + 2) = 0 . . . . (1)
Plane (1) is perpendicular to planes
2x + y – z – 2 = 0, x – y – z – 3 = 0
$\therefore$ 2a + b – c = 0 and a – b – c = 0
$\therefore \frac{a}{-2}=\frac{b}{1}=\frac{c}{-3}$
$\therefore$ Required plane is – 2(x – 1) + y – 3(z + 2) = 0
$\Rightarrow 2x-y+3z+4=0$