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If the planes x - cy - bz = 0, cx - y + az = 0 and bx + ay - z = 0 pass through a straight line, then the value of a² + b² + c² + 2abc is:

Option 1 -

-a

Option 2 -

0

Option 3 -

-1

Option 4 -

1

0 3 Views | Posted 3 weeks ago
Asked by Shiksha User

  • 1 Answer

  • R

    Answered by

    Raj Pandey | Contributor-Level 9

    3 weeks ago
    Correct Option - 4


    Detailed Solution:

      x - c y - b z = 0

    c x - y + a z = 0

    b x + a y - z = 0

    Equation of any plane passing through the line of intersection of planes (1) and (2)

    x - c y - b z + λ ( c x - y + a z ) = 0

    ( 1 + λ c ) x - ( c + λ ) y + ( - b + a λ ) z = 0

    If (3) &  (4) is same plane.

    1 + c λ b = - ( c + λ ) a = - b + a λ - 1

    (i)

    (ii) (iii)

    By (i)  & (ii) λ = - ( a + b c ) a c + b

    By (ii) & (iii)

    λ = - ( a b + c ) 1 - a 2 ; a 2 + b 2 + c 2 + 2 a b c = 1

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