Question

The equation of the plane through the point (0, –4, –6) and (–2, 9, 3) and perpendicular to the plane
x – 4y – 2z = 8 is

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

Answer 1

The correct option is C 2x + y – z = 2

Equation of plane through (0, –4, –6) is
a(x – 0) + b(y + 4) + c(z + 6) = 0 . . . .(i)
point (–2, 9, 3) lies on Eq. (i), then
– 2a + 13b + 9c = 0 . . . .(ii)
also required plane is perpendicular to x – 4y – 2z = 8
a – 4b – 2c = 0 . . . .(iii)
From Eqs. (i), (ii), (iii) we get
$\left|\begin{array}{ccc}x& y-4& z+6\\ -2& 13& 9\\ 1& -4& -2\end{array}\right|=0$
ie, 2x + y – z = 2