Question

If the equation of the plane $2x-3y+6z=7$ in the normal form is $lx+my+nz=p$ then $l+p$ equals

• A. $\frac{2}{7}$
• B. $\frac{9}{7}$
• C. $\frac{1}{7}$
• D. $\frac{3}{7}$

Answer 1

The correct option is B $\frac{9}{7}$

Equation of plane in the normal form is
$\frac{2x}{\sqrt{4+9+36}}+\frac{(-3)y}{\sqrt{4+9+36}}+\frac{6z}{\sqrt{4+9+36}}=\frac{7}{\sqrt{4+9+36}}$
$\Rightarrow \frac{2}{7}x-\frac{3}{7}y+\frac{6}{7}z=1\cdots \left(i\right)$
Given equation of plane in the normal form is
$lx+my+nz=p\cdots \left(ii\right)$
On comparing, we get
$l=\frac{2}{7},p=1$
$\therefore l+p=\frac{2}{7}+1=\frac{9}{7}$