Posted by Melissa on Saturday, April 7, 2012 at 1:53pm.
Explain fully please and thank you! =)
Determine the point of intersection of the lines L1: r= (1,3,7) + s(1,2,2),seR and L2: v=(0,2,3) +t(1,1,4), teR.
a) P(1,3,1)
b P(1,3,7)
c) The lines coincide
d) no point of intersection

Calculus  Reiny, Saturday, April 7, 2012 at 2:55pm
if they intersect:
s+1 = t+0 > t = s+1
and
2s+3 = t+2 > t = 2s+1
and
2s+7 = 4t3
using the first two equations
2s+1 = s+1
s = 0 , then t=1
test in 3rd equation ...
LS = 2s+7 = 0 + 7 = 7
RS = 4t3 = 43 = 1 ≠ LS
so they cannot intersect
Do they coincide?
If they did, they should have the same direction vectors ...
the first has direction (1,2,2) and the second has direction ( 1,1,4) , so they are not parallel
conclusion: We are looking at two lines which are not parallel and which do not intersect
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