Question

If the equation of a plane passing through the point $A(2,-3,7)$ and making equal intercepts on the axes is $x+y+z=p,$ then the value of $p$ is equal to

Answer 1

Let the required equation of the plane be$\frac{x}{a}+\frac{y}{a}+\frac{z}{a}=1\Rightarrow x+y+z=a$
Since,it passes through the point $A(2,-3,7)$, we have
$2+(-3)+7=a$
$\Rightarrow a=6$
Hence,the required equation of the plane is $x+y+z=6$
$\therefore p=6$