Question

The equation of the plane through the point (2, 5, –3) perpendicular to the planes x + 2y + 2z = 1 and x – 2y + 3z = 4 is

• A. 3x – 4y + 2z – 20 = 0
• B. 7x – y + 5z = 0
• C. x – 2y + = 11
• D. 10x – y – 4z = 27

Answer 1

The correct option is D 10x – y – 4z = 27

Equation of plane through (2, 5, –3) is
a(x – 2) + b(y – 5) + c(z + 3) = 0 . . . .(i)
which is perpendicular to
x + 2y + 2z = 1
and x – 2y + 3z = 4
then a + 2b + 2c = 0 . . . .(ii)
and a – 2b + 3c = 0 . . . .(iii)
Eliminating a, b, c from Eqs. (i), (ii) and (iii), we get
$\left|\begin{array}{ccc}x-2& y-5& z+3\\ 1& 2& 2\\ 1& -2& 3\end{array}\right|=0$
ie, 10x – y – 4z = 27 = 0