Question

Classify the following lines as either parallel, intersecting, coincident, or skew. In each case find the measure of the acute angle between them?

Answer 1

Answer:

The lines are parallel with an acute angle of 0 degrees.

Missing Information:

The equations of lines are missing which are as follows:

Line 1:

x = 1 - 2t , y = 8 + t, z = 5

Line 2:

x = 2 + 4s , y = -1 -2s, z = 3

Step-by-step explanation:

First, we need to find the direction vectors of both the line, we can write them as:

Direction Vector of line 1 =$D_{1}$= -2u + 1v + 0w

Direction Vector of line 2= $D_{2}$=4u -2v+0w

As we can see,

$D_{2}$=-2 $D_{1}$

such that:

4u -2v+0w= -2(-2u + 1v + 0w)

Since,

$D_{2}$=-2 $D_{1}$

So the lines are parallel such that θ= 0 degrees. (Which is the acute angle between them)

All the points on line 1 have z-coordinate as 5 (z=5),

All the points on line 2 have z-coordinate as 3 (z=3),

Since the z-coordinate do not match , so the lines are not coincident.

Also as the lines are parallel so they are not intersecting.