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Calculus

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7. Where does the line r = (1, 2, -5) + t (2, -3, 1) meet the plane 2x + 5y - 3z = 6?

  • Calculus - ,

    the line can be written as
    x = 1 + 2t
    y = 2 - 3t
    z = -5 + t

    sub that into your plane equation and see if it satisfies the equation

  • Calculus - ,

    slightly mis-read the question.

    continue from above

    2(1+2t) + 5(2-3t) - 3(-5+t) = 6
    2 + 4t + 10 - 15t + 15 - 3t = 6
    -14t = -21
    t = -21/-14 = 3/2

    x = 1 + 2(3/2) = 4
    y = 2 - 3(3/2) = -5/2
    z = -5 + 3/2 = -7/2

    the line intersects at (4, -5/2, -7/2)

  • Calculus - ,

    thanks reiny!

  • Calculus - ,

    welcome

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