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If the mirror image of the point (2, 4,7) in the plane 3x – y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to:

Option 1 -

54

Option 2 -

50

Option 3 -

-6

Option 4 -

-42

0 2 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • A

    Answered by

    alok kumar singh | Contributor-Level 10

    2 months ago
    Correct Option - 3


    Detailed Solution:

    Image of pt (2,4,7) in the plane 3x – y + 4z = 2 is

    x−23=y−4−1=z−74=−2 (6−4+28−2)32+ (−1)2+42

    Let x−23=y−4−1=z−74=−2813=λ

    x=3λ+2y=−λ+4z=4λ+7

    Now according to the question

    (a, b, c) =  (3λ+2, −λ+4, 4λ+7)

    Now 2a+b+2c=6λ+4−λ+4+8λ+14

    = 13λ+22

    = 28 + 22 [Use λ=−2813 ]

    = 6

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