Question

If $5,3,2$ are the direction ratios of a normal to the plane passing through the point $(2,3,1)$, then the sum of the intercepts made by the plane on the $x-$axis and $y-$axis is

• A. $\frac{8}{21}$
• B. $56$
• C. $\frac{56}{5}$
• D. $\frac{147}{10}$

Answer 1

The correct option is C $\frac{56}{5}$

The equation of the plane will be of the form $5x+3y+2z=d$
Since, the plane passes through $(2,3,1)$
$\Rightarrow 5\cdot 2+3\cdot 3+2\cdot 1=d$
$\Rightarrow d=21$
So, equation of plane is :
$\frac{x}{21/5}+\frac{y}{21/3}+\frac{z}{21/2}=1$
$\Rightarrow a=\frac{21}{5},b=7,\frac{21}{2}$
$\therefore a+b=\frac{56}{5}$