collision course

noun
1.
a course or path of a vehicle, projectile, etc., that, if unchanged, will lead to a collision with another object.
2.
any plan, attitude, or course of action that leads to a confrontation or conflict with another.

Origin:
1940–45

Dictionary.com Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2014.
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WordNet
collision course

noun
1. a course of a moving object that will lead to a collision if it continues unchanged 
2. a course of action (following a given idea) that will lead to conflict if it continues unabated 
WordNet® 3.0, © 2006 by Princeton University.
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Example sentences
In the case of one mile-wide space rock recently reported to be on a collision
  course with our planet, apparently not at all.
It has two probable escaped asteroids as moons with one on a collision course
  and the other moving slowly away.
The system also monitors your speed and trajectory to warn you if you're on a
  collision course.
The problem is that the existing technology puts us on a collision course with
  the environment.
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