Determine whether the lines L1 and L2 are parallel, skew, or intersecting. L1: x

Question

Determine whether the lines L1 and L2 are parallel, skew, or intersecting. L1: x = 1 + t, y = 2 - t, z = 3t L2: x = 2 - s, y = 1 + 2s, z = 4 + s parallel skew intersecting If they intersect, find the point of intersection. (If they do not intersect, enter NONE for each answer.) ( , , )

Determine whether the lines L1 and L2 are parallel, skew, or intersecting. L1: x = 1 + t, y = 2-t,z=3t L2: x = 2-s, y = 1 + 2s, z = 4 + s O parallel skew intersecting If they intersect, find the point of intersection. (If they do not intersect, enter NONE for each answer.)

Explanation / Answer

L1: x = 1 + t , y = 2 - t , z = 3t

L2: x = 2 - s , y = 1 + 2s , z = 4 + s

equating x coordinates

==> 1 + t = 2 - s

==> s +t = 1 ------- (1)

equating y coordinates

==> 2 - t = 1 + 2s

==> 2s + t = 1 ---- (2)

solving (1) and (2)

(1) - (2) ==> s +t -(2s +t) = 1 -1

==> s + t - 2s - t = 0

==> -s = 0

==> s = 0

==> t = 1 -s = 1 -0 = 1

now checking if s = 0 , t = 1 satsfy z - coordinate

==> 3(1) = 4 + 0

==> 3 = 4 (not true)

Hence The two lines are skew.

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