Question

Find the value of ${}^{\prime }{C}^{\prime }$ if sum of ${}^{\prime }{x}^{\prime }$ resistance ${}^{\prime }{y}^{\prime }$ intercept and ${}^{\prime }{x}^{\prime }$ intercept made by plane $2x-3y+5z+c=0$ on $x,y,z$ axis is $20$?

Answer 1

$2x-3y+5z+c=02x-3y+5z=-c\frac{x}{\frac{-c}{2}}+\frac{y}{\frac{c}{3}}+\frac{z}{\frac{-c}{5}}=1⟹\frac{-c}{2}+\frac{c}{3}+\frac{-c}{5}=20\frac{c}{30}(-15+10-6)=20-11c=600c=\frac{-600}{11}$