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The reflection of the point (2,-1,-3) in...

The reflection of the point (2,-1,-3) in the plane 3x - 2y -z = 9 is :

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line AB=`(x-2)/3=(y+1)/-2=(z-3)/-1=lambda`
`(x,y,z)=(3lambda+2,-2lambda-1,-lambda+3)`
`3x-2y-z=9`
`3(3lambda+2)-2(-2lambda-1)-3+lambda=9`
`9lambda+6+4lambda+2-3+lambda=9`
`14lambda=4`
`lambda=2/7`
`C(x,y,z)=(20/7,-11/7,19/7)`
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