The image of the line\frac{x-1}{3}= \frac{y-3}{1}= \frac{z-4}{-5} in the plane 2x -y+z +3 =0 is the line :

  • Option 1)

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

  • Option 2)

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

  • Option 3)

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

  • Option 4)

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

 

Answers (1)

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)

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

This option is incorrect

Option 2)

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

This option is incorrect

Option 3)

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

This option is correct

Option 4)

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

This option is incorrect

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