Question

Is the line through (-4, -6, 1) and (-2, 0, -3) parallel to the line through (5, 16, 5) and (2, 7, 11)?

A) Yes
B) No

Answer 1

The lines are parallel, so the answer is Yes.

Step-by-step explanation:

To determine if the lines are parallel, we can calculate the direction vectors of each line segment and see if they are scalar multiples of each other. The direction vector of the first line segment is (-2 - (-4), 0 - (-6), -3 - 1) = (2, 6, -4). The direction vector of the second line segment is (2 - 5, 7 - 16, 11 - 5) = (-3, -9, 6).Now, we can check if the direction vectors are scalar multiples of each other. If we divide the first component of the first direction vector by the first component of the second direction vector, we get 2/-3 = -2/3. If we divide the second component of the first direction vector by the second component of the second direction vector, we get 6/-9 = -2/3. If we divide the third component of the first direction vector by the third component of the second direction vector, we get -4/6 = -2/3.Since all three ratios are equal to -2/3, the lines are parallel. Therefore, the answer is A) Yes.