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.