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If the mirror image of the point $(2,4,7)$ in the plane $\mathrm{3 x-y+4 z=2}$ is $\mathrm{(a, b, c),}$ then $\mathrm{2 a+b+2 c}$ is equal to :
Option: 1
$54$

Option: 2
$50$

Option: 3
$-6$

Option: 4
$-42$

Answers (1)

best_answer

Using formula for mirror image

$\mathrm{\frac{a-2}{3}=\frac{b-4}{-1}=\frac{c-7}{4}=\frac{-2(6-4+28-2)}{9+1+16} }\\$

$\mathrm{\frac{a-2}{3}=\frac{b-4}{-1}=\frac{c-7}{4}=-\frac{1}{13}(28)}$

$\mathrm{a=2 -\frac{28 \times 3}{13}=\frac{-58}{13}} \\$

$\mathrm{b=4+\frac{28}{13}=\frac{80}{13}} \\$

$\mathrm{c=7-\frac{28 \times 4}{13}=-\frac{21}{13}} \\$

$\mathrm{\therefore 2 a+b+2 c=\frac{-116}{13}+\frac{80}{13}-\frac{42}{13} }\\$

$\mathrm{=-\frac{78}{13}=-6}$

Hence answer is option 3.

Posted by

Rakesh

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