Question

Equation of the plane through the points (2, 1, –1) and (–1, 3, 4) and perpendicular to the plane x + 2y + 4z = 0 is given by :

• A. 18x + 17y + 4z = 49
• B. 18x – 17y + 4z = 49
• C. 18x + 17y – 4z + 49 = 0
• D. 8x + 17y – 4z + 49 = 0

Answer 1

The correct option is A 18x + 17y + 4z = 49

Equation of the plane through (2, 1, –1) is
a(x – 2) + b(y – 1) + c(z + 1) = 0 . . .. .(1)
(1) passes through (–1, 3, 4) and is perpendicular to the plane x – 2y + 4z = 0, therefore
– 3a + 2b + 5x = 0 and a – 2b + 4c = 0
$\therefore \frac{a}{15}=\frac{b}{17}=\frac{c}{4}$
$\therefore$ Equation of plane is 18(x – 2) + 17(y – 1) + 4(z + 1) = 0
$\Rightarrow 18x+17y+4z=49$