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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.

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4 votes
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)
.
User Marklark
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