Lines and Planes: How Do They Intersect?

[Waking-Up]

Homework Statement

The Question Says:

Given tow lines and a plane:

The First Line is:L_1:(x y z):= (-4 3 4)*t +(7 2 -1)

The Second Line:L_2:(x y z):=( -3 5 5)*s +(-1 62 -11)

The Plane is :P:(x y z)dotted with(9 -2 3)=-4

(A)At which point do L_1 and P intersect? Check if this point lies in the plane P

(B) What is the shortest distance between L_1 and L_2?
The attempt at a solution:

For Part A

I have tried to do the following:

(-4*t+7)*(9)
(3*t+2)*(-2)
(4*t-1)*(3)
all equal to =-4

then solve for t
t=2

I am not sure if this is correct, for the next part "Check if this point lies in the plane P" I am not sure how to do so

for Part B I didn't try it yet , but I will do after a bit.

 

[hamsterman]

These line equations are parametric, so they say that if you choose any t (or s in L_2), you'll get a point on the line. The plane equations are implicit, so they say that for any point, if the equation is correct for it, that point is on the plane.
Now you have a method to generate a point on the line and a method to check if a point is on a plane. If you combine the two, you get an equation with a single unknown t. Since you're asked for a point, don't forget to generate it with the line function.