Find the plane determined by the intersecting lines (Calculus III Help)?

Hello,

need some help with this problem. my math is not coming out. PLEASE SHOW STEPS! Thanks so much for your help.

Find the plane determined by the intersecting lines L1 : x= -1 + t y= 2+t z = 1-t

L2: x= 1-4s y=1+2s z=2-2s

Answer: y+z=3

Thanks again!

2 Answers

  • x=-1+t

    y=2+t

    z=1-t

    ——–

    x=1-4s

    y=1+2s

    z=2-2s

    ———-

    -1+t=1-4s =>t=-4s+2

    2+t=1+2s

    4-4s=1+2s

    6s=3 =>s=1/2 =>t=0

    verify:

    1-t=2-2s

    1-0=2-1

    1=1 true

    the point of intersection is (-1,2,1)

    ———–

    the parametric form of the lines are:

    L1=(-1,2,1)+t(1,1,-1)

    L2=(1,1,2)+s(-4,2,-2)

    take the cross product of:

    <1,1,-1>*<-4,2,-2> = <0,6,6>

    as it passes through (-1,2,1) then:

    0(x+1)+6(y-2)+6(z-1)=0

    6y+6z=18

    y+z=3

  • Can you check your formula – this is not soluble.

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