Question

Equation of plane passing through the points

(2, 2, 1), (9, 3, 6) and perpendicular to plane

2x + 6y + 6z – 1 = 0 is –

• A. 3x + 4y + 5z = 9
• B. 3x + 4y – 5z = 9
• C. 3x + 4y + 5z + 9 = 0
• D. None of these

Answer 1

Answer: (B)

3x + 4y – 5z = 9

Answer 2

Any plane through (2, 2, 1) is

a (x – 2) + b(y – 2) + c(z – 1) = 0 …(1)

It passes through (9, 3, 6) if 7a + b + 5c = 0 …(2)

Also (1) is perpendicular to 2x + 6y + 6z – 1 = 0

\ 2a + 6b + 6c = 0 …(3)

\ from (2) and (3) : $\frac{a}{- 12} = \frac{b}{- 12} = \frac{c}{20}$ or $\frac{a}{3} = \frac{b}{4} = \frac{c}{- 5}$

\ equation of required plane is

3(x – 2) + 4(y – 2) – 5(z – 1) = 0

\ 3x + 4y – 5z – 9 = 0