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Let α, β and γ be real numbers such that the system of linear equations
x + 2y + 3 z = α
4x + 5y + 6z = β
7x + 8y + 9z = γ - 1
is consistent. Let |M| represent the determinant of the matrix

Let P be the plane containing all those α, β, γ for which the above system of linear equations is consistent, and D be the square of the distance of the point (0, 1, 0) from the plane P.
Q. The value of D is _____.
    Correct answer is '1.5'. Can you explain this answer?
    Most Upvoted Answer
    Let α, β andγbe real numbers such that the system of ...
    x + 2y + 3 z = α ... (1)
    4x + 5y + 6z = β ... (2)
    7x + 8y + 9z = γ - 1 ... (3)
    Adding equations (1) and (3) and subtracting two times equation (2):
    We get, 
    Plane P is x - 2y + z - 1 = 0.

    = 1.5
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    Let α, β andγbe real numbers such that the system of linear equationsx + 2y + 3 z =α4x + 5y + 6z =β7x + 8y + 9z = γ- 1is consistent. Let |M| represent the determinant of the matrixLet P be the plane containing all thoseα, β, γ for which the above system of linear equations is consistent, and D be the square of the distance of the point (0, 1, 0) from the plane P.Q.The value of D is _____.Correct answer is '1.5'. Can you explain this answer?
    Question Description
    Let α, β andγbe real numbers such that the system of linear equationsx + 2y + 3 z =α4x + 5y + 6z =β7x + 8y + 9z = γ- 1is consistent. Let |M| represent the determinant of the matrixLet P be the plane containing all thoseα, β, γ for which the above system of linear equations is consistent, and D be the square of the distance of the point (0, 1, 0) from the plane P.Q.The value of D is _____.Correct answer is '1.5'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let α, β andγbe real numbers such that the system of linear equationsx + 2y + 3 z =α4x + 5y + 6z =β7x + 8y + 9z = γ- 1is consistent. Let |M| represent the determinant of the matrixLet P be the plane containing all thoseα, β, γ for which the above system of linear equations is consistent, and D be the square of the distance of the point (0, 1, 0) from the plane P.Q.The value of D is _____.Correct answer is '1.5'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let α, β andγbe real numbers such that the system of linear equationsx + 2y + 3 z =α4x + 5y + 6z =β7x + 8y + 9z = γ- 1is consistent. Let |M| represent the determinant of the matrixLet P be the plane containing all thoseα, β, γ for which the above system of linear equations is consistent, and D be the square of the distance of the point (0, 1, 0) from the plane P.Q.The value of D is _____.Correct answer is '1.5'. Can you explain this answer?.
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