If the line passing through the points and is parallel to the line passing through the points and , what is the value of a?

Question

If the line passing through the points  and  is parallel to the line passing through the points  and  , what is the value of a?

Quizplus · Accepted Answer

If two lines are parallel, their direction vectors are parallel. Let's find the direction vectors of these two lines: 
First line: (11eaa8b1_dcc7_a2b5_b1b6_db50a6ac1893_TB6026_11) - (11eaa8b1_dcc7_7ba4_b1b6_153b2b8615e5_TB6026_11) = (0, dccd, 0, 0, 0, 0, 0, a2b5-db50a6ac1893, 0, 0, 0) 
Second line: (11eaa8b1_dcc7_c9c7_b1b6_5722c3cdf231_TB6026_11) - (11eaa8b1_dcc7_a2b6_b1b6_d713c1d83234_TB6026_11) = (0, dcc1, 0, 0, 0, 0, 0, c9c7-a2b6, 0, 0, 0) 
For these two vectors to be parallel, the ratio of their components must be the same. For example, (a2b5-db50a6ac1893)/(c9c7-a2b6) = dccd/dcc1. 
Therefore, we can solve for a: (db50a6ac1893-a2b5)/(c9c7-a2b6) = dccd/dcc1. Plugging in the given values, we get: 
(a-3efb)/(17ea-a) = (f0d9-f0d8)/(f0d8-f0d7) 
Solving for a, we get a = 11eaa8b1_dcc7_f0d9_b1b6_93aab7fed577_TB6026_11.

If the Line Passing Through the Points and