Question

L1: x=−2t, y=1+2t, z=3tl1: x=−2t, y=1+2t, z=3t and l2: x=−9+5s, y=5s, z=2+4sl2: x=−9+5s, y=5s, z=2+4s find the point of intersection of the two lines.

Answer 1

Hello : 
L1: x=−2t, y=1+2t, z=3t........(1)
l2: x=−9+5s, y=5s, z=2+4s....(2)
by(1) and(2) :
-2t =-9+5s....(*)
1+2t = 5s.... (**)
3t = 2+4s.... (***)
by (*) : 5s = 9 - 2t
by(**) : 5s = 1+2t
1+2t = 9 - 2t
4t = 8
t = 2
sunsct in (***) : 3(2) = 2+ 4s 
4s =4
s= 1
subsct  s  and t in : L1 or L2
in : L2.....s=1
 x = -9+5 = -4
y = 5
z=2+4 = 6
same calcul in : L1    ... t = 2
x = -2(2) = -4
y = 1+2(2) = 5
z = 3(2) =6
conclusion : 
find the point of intersection of the two lines is : (-4 , 5 , 6)
.