Question

If the plane $x-3y+5z=d$ passes through the point $(1,2,4)$ then the intercepts on $x,y,z$ axes respectively are:

• A. $15,-5,3$
• B. $1,-5,3$
• C. $-15,5,-3$
• D. $1,-6,20$

Answer 1

The correct option is A $15,-5,3$

The plane $x-3y+5z=d$ passes through the point $(1,2,4)$
Therefore the point $(1,2,4)$ satisfies the above equation.
$\therefore 1-6+20=d\Rightarrow d=15$
Hence, $x-3y+5z=15$
$\Rightarrow \frac{x}{15}+\frac{y}{-5}+\frac{z}{3}=1$
$\therefore$The intercept on $x,y,z$ axes are $15,-5,3$