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Mirror image of a point in a plane with unknowns in the point or the plane: find them

The same question, asked 2 times: 2021 Paper 10*, 27 Jun 2022. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 10

    86
    Let the mirror image of the point (1,3,a)(1,3,a) with respect to the plane r→⋅(2i^−j^+k^)−b=0\overrightarrow{r}\cdot (2\widehat{i}-\widehat{j}+\widehat{k}) - b = 0 be (−3,5,2)( - 3,5,2). Then the value of ∣a+b∣|a+b| is equal to

  2. Question 2

    27 Jun 2022

    90
    Let the mirror image of the point (a,b,c)(a,b,c) with respect to the plane 3x−4y+12z+19=03x - 4y + 12z + 19 = 0 be (a- 6,β,γ)6,\beta,\gamma). If a+b+c=5a + b + c = 5, then 7β−9γ7\beta - 9\gamma is equal to