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Equation of a plane passing through point with position vector a and having normal n is
A(r − a) · n = 0
Br × n = a (typical)
Cr + n = a
Dr · a = n
Answer & Solution
Correct answer: A. (r − a) · n = 0
1. A plane is uniquely determined by a point on it and a normal to it.
2. Any vector r − a in the plane must be perpendicular to the normal n.
3. So (r − a) · n = 0 is the vector equation.
_Source: Maharashtra Balbharati Std XII Mathematics Part 1, Ch 6 "Line and Plane" §6.5_
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