Question

If the foot of the perpendicular from the origin to a plane is

(a, b, c), then equation of the plane is –

• A. $\frac{x}{a} + \frac{y}{b} + \frac{z}{c}$ = 1
• B. ax + by + cz = 1
• C. ax + by + cz = a² + b² + c²
• D. ax + by + cz = 0

Answer 1

Answer: (D)

ax + by + cz = 0

Answer 2

Let P be the foot of the perpendicular from the origin on the plane then direction ratios of OP, the normal to the plane are a – 0, b – 0, c – 0, i.e. a, b, c. Also since it passes through

(a, b, c), the equation of the plane is

a(x – a) + b(y – b) + c (z – c) = 0

Ž ax + by + cz = a² + b² + c².