find the image of point (1,2,3) in the plane 3x+2y-z=8

let Q be the image of the point P(1, 2, 3) in the plane 3x+2y-z = 8.

then PQ is normal to the plane. therefore , direction ratios of PQ are 3, 2,-1.

since PQ passes through P(1,2,3) and has direction ratios 3,2,-1.

therefore the equation of PQ is .

let the coordinates of Q be .

let R be the mid point of PQ. then R, lies on the plane 3x+2y-z = 8.

the coordinates of R are:

since R lies on 3x+2y-z = 8

therefore

hence the coordinates of Q are

i.e.

hope this helps you.

cheers!!

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