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Mirror image of a point in a plane

This type of question, asked 5 times: 4 May 2023 S2, 10 May 2024 S1, 14 May 2024 S2, 26 Apr 2025 S1, 13 May 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    108
    Let P be a plane passing through the points (2,1,0),(4,1,1)(2,1,0),(4,1,1) and (5,0,1)(5,0,1) and R be the point (2,1,6)(2,1,6). Then image of R in the plane P is

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  2. Question 2

    10 May 2024 S1

    113
    Plane P through (2,1,0),(4,1,1),(5,0,1). Image of R(2,1,6) in plane P is

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  3. Question 3

    14 May 2024 S2

    148
    The mirror image of P(2,4,−1)P(2,4,-1) in the plane x−y+2z−2=0x-y+2z-2=0 is (a,b,c)(a,b,c), then the value of a+b+ca+b+c is

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  4. Question 4

    26 Apr 2025 S1

    132
    The mirror image of the point P(−1,2,−4)P( - 1,2, - 4) in the plane x−y−2z+1=0x-y- 2z+ 1 = 0 is

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  5. Question 5

    13 May 2026 S2

    94
    If the point Q(α,β,γ)Q(\alpha, \beta, \gamma) is the mirror image of P(10,15,20)P(10, 15, 20) in the plane r⃗=k^+λ(−i^+j^)+μ(−i^+k^)\vec{r} = \hat{k} + \lambda(-\hat{i} + \hat{j}) + \mu(-\hat{i} + \hat{k}), λ,μ∈R\lambda, \mu \in \mathbb{R} then the value of 3(α+β+γ)3(\alpha + \beta + \gamma) is

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