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Math Help - Parametric form for the straight line

  1. #1
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    Question Parametric form for the straight line

    Check that r0 = (0, 4/3, -5/3) is a point on the intersection of the planes
    3x + y - z = 3, x + 2y + 4z = -4.
    Hence find a parametric form for the straight line defined by intersection of these planes.
    HINT: use the fact that the line must pass through r0 and be perpendicular to the normal of each plane.
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  2. #2
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    Hello, njr008!

    (a) Check that r_0 \:= \:\left(0,\:\frac{4}{3},\:-\frac{5}{3}\right) is a point on the intersection of the planes:

    . . 3x + y - z \:= \:3\;\text{ and }\;x + 2y + 4z \:=\: -4
    Substitute the coordinates into the equations of the planes
    . . and show that r_o lies on both planes.



    (b) Find the parametric equations for the straight line
    defined by intersection of these planes.

    HINT: use the fact that the line must pass through r_0
    and be perpendicular to the normal of each plane.
    Find the direction vector of the line with: . \langle3,1,-1\rangle \times \langle1,2,4\rangle

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