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These vehicles are driving along a one-way road with three lanes. Cars A and B are both planning to change lane. Which car has right of way here?

A Car A

When two cars are attempting to merge into the same lane, the car on the left has right of way, i.e. give way to your left when merging. So, if you are merging into an empty lane to your right, you theoretically have right of way. However, you should never just assume that other drivers will yield. [Driving on Multiple-Lane Roads, Right-of-Way at Intersections, Chapter 4: Right-of-Way, Texas Driver's Handbook]