Question

Determine whether the lines and are parallel, skew, or intersecting. if they intersect, find the point of intersection.

L₁:x= 12+8t, y=16-4t, z=4=12t
L₂:x= 4+16s, y=12-8s, z=16+20s
A)parallel
B)skew
C)intersecting

Answer 1

The given lines are skew.

Step-by-step explanation:

The given lines can be represented by the parametric equations:

L₁: x = 12 + 8t, y = 16 - 4t, z = 4 + 12t

L₂: x = 4 + 16s, y = 12 - 8s, z = 16 + 20s

To determine whether the lines are parallel, skew, or intersecting, we can compare the direction vectors of the lines. The direction vectors of L₁ and L₂ are [8, -4, 12] and [16, -8, 20] respectively.

If the direction vectors are scalar multiples of each other, the lines are parallel. If they are not multiples of each other and not orthogonal, the lines are skew. If they are orthogonal, the lines intersect.

In this case, the direction vectors are not multiples of each other and not orthogonal, which means the lines are skew. Therefore, the answer is B) skew.