Q. Through the point $P($α,β,γ) a plane is drawn at right angles to $OP$ to meet the coordinate axes are $A,B,C$ respectively. If $OP = p$ then equation of plane $\overrightarrow{A,B,C}$ is
A) $\alpha x + \beta y + \gamma z = p$
B) $\frac{x}{\alpha} + \frac{y}{\beta} + \frac{z}{\gamma} = p$
C) $2\alpha x + 2\beta y + 2\gamma z = p^{2}$
D) $\alpha x + \beta y + \gamma z = p^{2}$
Explanation
(a)
$Equation\ of\ plane\ is\ \overrightarrow{\mathbf{r}} \bullet \widehat{\mathbf{n}} = d,$
where $d$ is the perpendicular distance of the plane from origin
$\therefore Required\ plane\ is\ (\alpha x + \beta y + \gamma z) = p\$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.