Question

If from the point P(a, b, c) perpendiculars PL, PM be drawn to YOZ and ZOX planes, then the equation of the plane OLM is

• A. $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=0$
• B. $\frac{x}{a}-\frac{y}{b}+\frac{z}{c}=0$
• C. $\frac{x}{a}+\frac{y}{b}-\frac{z}{c}=0$
• D. $\frac{x}{a}-\frac{y}{b}-\frac{z}{c}=0$

Answer 1

The correct option is C $\frac{x}{a}+\frac{y}{b}-\frac{z}{c}=0$

Coordinates of L and M are (0, b, c) and (a, 0, c) respectively.
$\therefore$ Equation of plane through (0, 0, 0), (0, b, c) and (a, 0,c) is
$\left|\begin{array}{ccc}x-0& y-0& z-0\\ 0& b& c\\ a& 0& c\end{array}\right|$
i.e., $\frac{x}{a}+\frac{y}{b}-\frac{z}{c}=0$