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Points (1,1,m) and (-3,0,1) are equidistant from the plane 3x + 4y - 12z + 13 = 0: find m

The same question, asked 2 times: 4 May 2023 S2*, 11 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    4 May 2023 S2

    102
    If the points (1,−1,λ)(1,-1,\lambda) and (−3,0,1)(-3,0,1) are equidistant from the plane 3x−4y−12z+13=03x-4y-12z+13=0, then the sum of all possible values of λ\lambda is

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  2. Question 2

    11 Apr 2026 S1

    93
    If the points (1,1,μ)(1, 1, \mu) and (−3,0,1)(-3, 0, 1) are equidistant from the plane r⃗⋅(3i^+4j^−12k^)+13=0\vec{r}\cdot(3\hat{i} + 4\hat{j} - 12\hat{k}) + 13 = 0, then the value of μ\mu are

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