Are the given lines parallel, intersecting, identical or skew? $\vec { r } _ { 1 } ( t ) = \langle 2,3,6 \rangle + t \langle - 1,2,4 \rangle$ $\vec { r } _ { 2 } ( t ) = \langle 9 , - 1 , - 2 \rangle + t \langle 2 , - 4 , - 8 \rangle$
A) Parallel
B) Identical
C) Intersecting
D) Skew

Question

Quizplus · Accepted Answer

The direction vectors of the given lines are $\langle -1, 2, 4 \rangle$ for the first line and $\langle 2, -4, -8 \rangle$ for the second line. The second direction vector is a scalar multiple of the first ($2 \times \langle -1, 2, 4 \rangle = \langle 2, -4, -8 \rangle$), indicating that the lines are parallel. They are not identical because their points do not match, and they do not intersect at any point, making them parallel but distinct lines.

Are the Given Lines Parallel, Intersecting, Identical or Skew r⃗1(t)=⟨2,3,6⟩+t⟨−1,2,4⟩\vec { r } _ { 1 } ( t ) = \langle 2,3,6 \rangle + t \langle - 1,2,4 \rangler1​(t)=⟨2,3,6⟩+t⟨−1,2,4⟩

Are the Given Lines Parallel, Intersecting, Identical or Skew $\vec { r } _ { 1 } ( t ) = \langle 2,3,6 \rangle + t \langle - 1,2,4 \rangle$