Question

Through the point $P(\alpha ,\,\beta ,\,\,\gamma )$ 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 $ABC$ is

• A. $\alpha x+\beta y+\gamma z=p$
• B. $\frac{x}{\alpha }+\frac{x}{\beta }+\frac{z}{\gamma }=p$
• C. $2\alpha x+2\beta y+2\gamma z={{p}^{2}}$
• D. $\alpha x+\beta y+\gamma z={{p}^{2}}$

Answer 1

Answer: (A)

$\alpha x+\beta y+\gamma z=p$

Answer 2

Equation of plane is $\vec{r}\,.\hat{n}=d$
Where d is the perpendicular distance of the plane from origin.
$\Rightarrow$ $\alpha x+\beta y+\gamma z=0$