# The image of the line in the plane is the line : Option 1) Option 2) Option 3) Option 4)

As we learnt in

Image of a point -

Let $L'$ be the image of point $P\left ( \alpha ,\beta ,\gamma \right )$ in the plane $ax+by+cz+d=0$

$L'$ will be given by the formula

$\frac{x-\alpha }{a}=\frac{y-\beta }{b}=\frac{z-\gamma }{c}= \frac{-2\left ( a\alpha +b\beta +c\gamma +d \right )}{a^{2}+b^{2}+c^{2}}$

-

Image of (1,3,4) in plane is

$\frac{x-1}{2}= \frac{y-3}{-1}= \frac{z-4}{1} = \frac{-2\left ( 2-3+4+3 \right )}{2^{2}+^{1^{2}}+1^{2}}\\ \frac{x-1}{2}= \frac{y-3}{-1}= \frac{z-4}{1}= -2\\x=-3; y=5, z=2$

So equation of line is

$\frac{x+3}{3}= \frac{y-5}{1}=\frac{z-2}{-5}$

Option 1)

This option is incorrect

Option 2)

This option is incorrect

Option 3)

This option is correct

Option 4)

This option is incorrect

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