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 = 4t-3

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 = 4t-3 = 4-3 = 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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