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. $\frac{217}{10}$

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 $(2,3,1)$

$d=21$

Intercepts along the axes are $\frac{21}{5},7,\frac{21}{2}$ respectively.

Their sum of $x$-axis and $y$-axis intercepts is $\frac{56}{5}$.