Question

Consider two intersecting lines L1 and L2:

The line L1 is given by x(t)=1−3t,y(t)=1t,z(t)=3+1t.
The line L2 parallel to the vector <11,3,7> through the point (−8,3,6).
What is the point of intersection?

Answer 1

where are you getting the variable s from?

Answer 2

L2 = s<11,3,7> + <-8,3,6?

Answer 3

i had a typo, so let me rephrase:
x2 = 11s - 8
y2 = 3s + 3
z2 = 7s + 6

Answer 4

Then how do solve for both t and s if no equation has be variables?

Answer 5

well, if the two lines interest, then their coordinate are the same. I.e
x1 = x2
y1 = y2
z1 = z1

where x1,y1,z1 are the components of L1
and x2,y2,z2 are the components of L2