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

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 == -2u + 1v + 0w

Direction Vector of line 2= =4u -2v+0w

As we can see,

=-2

such that:

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

Since,

=-2

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.

Because we have been given the slope and y-intercept, we can create an equation in slope-intercept form.

y = mx + b

m = the slope

b = y-intercept.

In the first problem,

m = -4

b = 10

So, our equation looks like: y = -4x + 10

In the second problem,

m = 1/3

b = -6

So, our equation looks like: y = 1/3x - 6