Posted by **Gunjan kumar** on Sunday, January 23, 2011 at 7:29am.

Show the two lines (x/2-1/2)=(y/3-2/3)=(z/4-3/4) and (x/5-4/5)=z intersect.find the point of intersection of these lines

- Math -
**Reiny**, Sunday, January 23, 2011 at 9:03am
subbing the 2nd into the first:

x/2 - 1/2 = z/4 - 3/4

x/2 - 1/2 = (1/4)(x/5-4/5) - 3/4

times 4

2x - 2 = (x/5 - 4/5) - 3

times 5

10x - 10 = x - 4 - 15

9x = -9

x = -1

into z = x/5 - 4/4 = -1/5 - 4/5 = -1

z = -1

lastly

y/3 - 2/3 = z/4 - 3/4

y/3 - 2/3 = -1/4-3/4

y/3 - 2/3 = -1

times 3

y - 2 = -3

y = -1

they intersect at (-1, -1, -1)

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