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25 August, 13:37

Find a set of parametric equations for the line of intersection of the planes 3x-2y-z=7 x-4y+2z=0

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  1. 25 August, 13:48
    0
    equation of the line is

    L (x, y, z) = (0,-7/4,-7/2) + (2,7/4, 5/2) * t, where t is the parameter

    Step-by-step explanation:

    for the planes

    3x-2y-z=7

    x-4y+2z=0

    multiplying by 2 the first equation and summing both equations

    7x-8y=14

    for y=0, x=2 → z = - 1 (replacing in any plane equation)

    for x=0, y=-7/4 → z=-7/2 (replacing in any plane equation)

    then (2,0,-1) and (0,-7/4,-7/2) belongs to the line → thus one parallel vector to the line is

    v = (2,0,-1) - (0,-7/4,-7/2) = (2,7/4, 5/2)

    the parametric equation of the line is

    L (x, y, z) = (0,-7/4,-7/2) + (2,7/4, 5/2) * t, where t is the parameter

    Note

    for t=0 → L (x, y, z) = (0,-7/4,-7/2)

    for t=1 → L (x, y, z) = (2,0,-1)
  2. 25 August, 13:49
    0
    To find a set of parametric equations for the line of intersection of the planes 3x+2y-z=7 eqn1

    x-4y+2z=0 eqn2

    Mulitply eqn 1 by 2, to solve this simultaneously

    6x+4y-2z=14 eqn3

    x - 4y+2z=0

    Add eqn 3 to eqn 2, we have

    7x = 14

    x = 2, put this into eqn2 and assume y = v

    2 - 4v + 2z = 0

    2z = 4v-2, z=2v-1

    Hence, a set of parametric equations are x = 2, y = v and z=2v-1
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