Question

If the sum of the reciprocals of the intercepts made by the plane $ax+by+cz=1$ on the three axes is $1$, then the plane always passes through the point

• A. $(2,-1,0)$
• B. $(1,1,1)$
• C. $(-1,-1,-1)$
• D. $(1/2,-1,1/2)$

Answer 1

Answer: (B)

$(1,1,1)$

Plane:$ax+by+cz=1x=\frac{1}{a},y=\frac{1}{b},z=\frac{1}{c}$

$\therefore \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=a+b+c=1$(Since sum of reciprocal of intercets is $\perp$)

$\therefore a+b+c=1-\left(i\right)$

Comparing $\left(i\right)$ with plane equation,

$(x,y,z)=(1,1,1)$ satisfies plane always.