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Math

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Show the two lines (x/2-1/2)=(y/3-2/3)=(z/4-3/4) and (x/5-4/5)=z intersect.find the point of intersection of these lines

  • Math -

    subbing the 2nd into the first:
    x/2 - 1/2 = z/4 - 3/4
    x/2 - 1/2 = (1/4)(x/5-4/5) - 3/4
    times 4
    2x - 2 = (x/5 - 4/5) - 3
    times 5
    10x - 10 = x - 4 - 15
    9x = -9
    x = -1

    into z = x/5 - 4/4 = -1/5 - 4/5 = -1
    z = -1

    lastly
    y/3 - 2/3 = z/4 - 3/4
    y/3 - 2/3 = -1/4-3/4
    y/3 - 2/3 = -1
    times 3
    y - 2 = -3

    y = -1

    they intersect at (-1, -1, -1)

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