Question

If O is the origin and A is the point (a, b, c) then the equation of the plane through A and at right angles to OA is

• A. $a(x - a) - b(y - b) - c(z - c) = 0$
• B. $a(x + a) + b(y + b) + c(z + c) = 0$
• C. $a(x - a) + b(y - b) + c(z - c) = 0$
• D. None of these

Answer 1

Answer: (C)

$a(x - a) + b(y - b) + c(z - c) = 0$

Answer 2

Normal will be OA whose direction ratios are $a - 0$ $b - 0$ $c - 0$ i.e., a, b, c. It passes through $A ( a , b , c )$

$\therefore$ Equation of required plane is, $a ( x - a ) + b ( y - b ) + c ( z - c ) = 0$.