Question

Determine if the lines given intersect, are parallel or are skew. l1: x = 1/5(y - 2/4) = (z - 3)/(-3) and l2: x = 1/6(y - 2/3) = (z - 3)/(2/3)

Answer 1

The given lines are skew.

Step-by-step explanation:

To determine if the given lines intersect, parallel, or skew, we need to compare the equations of the lines. Let's start by simplifying the equations of the lines:

For l1: x = ⅓(y - ⅓) = −⅓(z - 3)

For l2: x = ⅓(y - ⅔) = (z - 3)/(/⅕)

Now, we can compare the coefficients of the variables. If the ratios of the coefficients are different, then the lines are skew. If the ratios are the same, then the lines are either intersecting or parallel. By comparing the coefficients, we see that the ratios are different. Therefore, the lines are skew and do not intersect or parallel to each other.