Question

Equation of the plane perpendicular to the plane x – 2y + 5z + 1 = 0 which passes through the points (2, –3, 1) and (–1, 1, –7) is given by :

• A. 4x – 4y + z + 7 = 0
• B. 4x + 7y + 2z + 11 = 0
• C. 2x + y – z = 0
• D. 2x + y – 3z = 0

Answer 1

The correct option is B 4x + 7y + 2z + 11 = 0

Equation of the plane through (2, –3, 1) is
a(x – 2) + b(y + 3) + c(z – 1) = 0
It passes through (–1, 1, –7) and perpendicular to the plane x – 2y + 5z + 1 = 0
$\therefore$ –3a+ 4b – 8c = 0 and a – 2b + 5c = 0
$\therefore \frac{a}{4}=\frac{b}{7}=\frac{c}{2}$
Hence, equation of required plane is
4x + 7y + 2z + 11 = 0