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Mirror image of a point in a plane

This type of question, asked 11 times: 2021 Paper 10, 2021 Paper 21, 2021 Paper 26, 25 Jun 2022, 27 Jun 2022, 29 Jun 2022, 1 Feb 2023, 8 Apr 2023, 10 Apr 2023, 11 Apr 2023, 13 Apr 2023. All 12 questions below, oldest first.

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  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

    2021 Paper 21

    82
    Let SS be the mirror image of the point Q(1,3,4)Q(1,3,4) with respect to the plane 2x−y+z+3=02x - y + z + 3 = 0 and let R(3,5,γ)R(3,5,\gamma) be a point of this plane. Then the square of the length of the line segment SRSR is

  3. Question 3

    2021 Paper 26

    78
    If the mirror image of the point (1,3,5)(1,3,5) with respect to the plane 4x−5y+2z=84x- 5y+ 2z= 8 is (α,β,γ)(\alpha,\beta,\gamma), then 5(α+β+γ)5(\alpha+\beta+\gamma) equals:

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  4. Question 4

    25 Jun 2022

    77
    Let QQ be the mirror image of the point P(1,0,1)P(1,0,1) with respect to the plane S:x+y+z=5S:x + y + z = 5. If a line LL passing through (1,−1,−1)(1, - 1, - 1), parallel to the line PQ meets the plane SS at RR, then QR2QR^{2} is equal to:

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  5. Question 5

    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

  6. Question 6

    29 Jun 2022

    63
    If the mirror image of the point (2,4,7)(2,4,7) in the plane 3x−y+4z=23x - y + 4z = 2 is (a,b,c)(a,b,c), the 2a+b+2c2a + b + 2c is equal to :

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  7. Question 7

    1 Feb 2023

    74
    Let the image of the point P(2,−1,3)P(2, - 1,3) in the plane x+2y−z=0x + 2y - z = 0 be QQ. Then the distance of the plane 3x+2y+z+29=03x + 2y + z + 29 = 0 from the point QQ is

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  8. Question 8

    8 Apr 2023

    153
    Let PP be the plane passing through the line x−11=y−2−3=z+57\frac{x - 1}{1}=\frac{y - 2}{- 3}=\frac{z + 5}{7} and the point (2,4,−3)(2,4, - 3). If the image of the point (−1,3,4)( - 1,3,4) in the plane PP is (α,β,γ)(\alpha,\beta,\gamma), then α+β+γ\alpha + \beta + \gamma is equal to

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  9. Question 9

    10 Apr 2023

    76
    Let two vertices of triangle ABCABC be (2,4,6)(2,4,6) and (0,−2,−5)(0, - 2, - 5), and its centroid be (2,1,−1)(2,1, - 1). If the image of third vertex in the plane x+2y+4z=11x + 2y + 4z = 11 is (α,β,γ)(\alpha,\beta,\gamma), then αβ+βγ+γα\alpha\beta + \beta\gamma + \gamma\alpha is equal to

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  10. Question 10

    10 Apr 2023

    154
    Let the image of the point P(1,2,6)P(1,2,6) in the plane passing through the points A(1,2,0),B(1,4,1)A(1,2,0),B(1,4,1) and C(0,5,1)C(0,5,1) be Q(α,β,γ)Q(\alpha,\beta,\gamma). Then (α2+β2+γ2)\left( \alpha^{2}+\beta^{2}+\gamma^{2} \right) is equal to:

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  11. Question 11

    11 Apr 2023

    77
    Let (α,β,γ)(\alpha,\beta,\gamma) be the image of the point P(2,3,5)P(2,3,5) in the plane 2x+y−3z=62x + y - 3z = 6. Then α+β+γ\alpha + \beta + \gamma is equal to

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  12. Question 12

    13 Apr 2023

    88
    Let the image of the point (53,53,83)\left( \frac{5}{3},\frac{5}{3},\frac{8}{3} \right) in the plane x−2y+z−2=0x - 2y + z - 2 = 0 be PP. If the distance of the point Q(6,−2,α),α>0Q(6, - 2,\alpha),\alpha > 0, from PP is 13 , then α\alpha is equal to