Prove the following


If $(\mathrm{x}, \mathrm{y}, \mathrm{z})$ be an arbitrary point lying on a plane $\mathrm{P}$ which passes through the point $(42,0,0)(0,42,0)$ and $(0,0,42)$, then the value of expression




  1. (1) 0

  2. (2) 3

  3. (3) 39

  4. (4) $-45$

Correct Option: , 2


Plane passing through $(42,0,0),(0,42,0)$,


From intercept from, equation of plane is



let $\quad a=x-11, b=y-19, c=z-12$


Now, given expression is

$3+\frac{a}{b^{2} c^{2}}+\frac{b}{a^{2} c^{2}}+\frac{c}{a^{2} b^{2}}-\frac{42}{14 a b c}$

$3+\frac{a^{3}+b^{3}+c^{3}-3 a b c}{a^{2} b^{2} c^{2}}$

If $a+b+c=0$

$\Rightarrow a^{3}+b^{3}+c^{3}=3 a b c$

$\Rightarrow 3$

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